3
Moduli Spaces
http://sms.cam.ac.uk/collection/1087487
Algebraic geometry is a key area of mathematical research of international significance. It has strong connections with many other areas of mathematics (differential geometry, topology, number theory, representation theory, etc.) and also with other disciplines (in the present context, particularly theoretical physics). Moduli theory is the study of the way in which objects in algebraic geometry (or in other areas of mathematics) vary in families and is fundamental to an understanding of the objects themselves. The theory goes back at least to Riemann in the midnineteenth century, but moduli spaces were first rigorously constructed in the 1960s by Mumford and others. The theory has continued to develop since then, perhaps most notably with the infusion of ideas from physics after 1980.
Read more at: http://www.newton.ac.uk/programmes/MOS/
1440
2016
Wed, 01 Jun 2016 11:32:24 +0100
Wed, 05 Jan 2011 18:04:39 +0000
en
smssupport@uis.cam.ac.uk
Moduli Spaces
http://sms.cam.ac.uk/collection/1087487
http://rss.sms.cam.ac.uk/itunesimage/1393862.jpg
http://video.search.yahoo.com/mrss
Moduli Spaces
Algebraic geometry is a key area of mathematical research of international significance. It has strong connections with many other areas of mathematics (differential geometry, topology, number theory, representation theory, etc.) and also with other disciplines (in the present context, particularly theoretical physics). Moduli theory is the study of the way in which objects in algebraic geometry (or in other areas of mathematics) vary in families and is fundamental to an understanding of the objects themselves. The theory goes back at least to Riemann in the midnineteenth century, but moduli spaces were first rigorously constructed in the 1960s by Mumford and others. The theory has continued to develop since then, perhaps most notably with the infusion of ideas from physics after 1980.
Read more at: http://www.newton.ac.uk/programmes/MOS/
Moduli Spaces
Algebraic geometry is a key area of mathematical research of international significance. It has strong connections with many other areas of mathematics (differential geometry, topology, number theory, representation theory, etc.) and also with other disciplines (in the present context, particularly theoretical physics). Moduli theory is the study of the way in which objects in algebraic geometry (or in other areas of mathematics) vary in families and is fundamental to an understanding of the objects themselves. The theory goes back at least to Riemann in the midnineteenth century, but moduli spaces were first rigorously constructed in the 1960s by Mumford and others. The theory has continued to develop since then, perhaps most notably with the infusion of ideas from physics after 1980.
Read more at: http://www.newton.ac.uk/programmes/MOS/
Cambridge University
Steve Greenham
http://sms.cam.ac.uk/collection/1087487
Moduli Spaces
20110105T18:04:39+00:00
INIMS
101092
no

(k,l)stability
ucs_sms_1087487_1097723
http://sms.cam.ac.uk/media/1097723
(k,l)stability
Mata Gutierrez, O (CIMAT)
Thursday 10 February 2011, 15:3016:30
Mon, 14 Feb 2011 15:29:26 +0000
Mata Gutierrez, O
Steve Greenham
Isaac Newton Institute
Mata Gutierrez, O
60ba0bd9ea5959fc3d9de3e03a91e485
5978726d46b57d587bc0db4865fe017c
c6ff481939d86dcc6cf5d4bfedee930f
Mata Gutierrez, O (CIMAT)
Thursday 10 February 2011, 15:3016:30
Mata Gutierrez, O (CIMAT)
Thursday 10 February 2011, 15:3016:30
Cambridge University
3319
http://sms.cam.ac.uk/media/1097723
(k,l)stability
Mata Gutierrez, O (CIMAT)
Thursday 10 February 2011, 15:3016:30
Narasimhan and Ramanan introduced the concept of (k,l)stability for vector bundles over projective curves. They used the (0,1) and (1,1)stability to compute the deformations of the moduli space M(n,d) of stable vector bundles and to define the Hecke cycles. In this lecture I will present some properties of (k,l)stability for any k and l and describe the set A(k,l) of (k,l)stable in terms of the Segre invariants. For certain values of k and l I will give the relation between A(k,l) and the Hilbert scheme of M(n,d).
20110214T15:29:31+00:00
3319
1097723
true
16x9
false
no

A compactification for the moduli stack of bundles on a surface
ucs_sms_1087487_1095962
http://sms.cam.ac.uk/media/1095962
A compactification for the moduli stack of bundles on a surface
Baranovsky, V (University of California, Irvine)
Tuesday 01 February 2011, 11:0012:30
Tue, 08 Feb 2011 13:53:02 +0000
108
108100
Baranovsky, V
Steve Greenham
University of Cambridge
Steve Greenham
534b8f54f684da28c1c889ec8370fd9c
a788bd53d05c766b4be4fa282b05a597
8e083dfc7810333727caf3a1fb8df534
Baranovsky, V (University of California, Irvine)
Tuesday 01 February 2011,...
Baranovsky, V (University of California, Irvine)
Tuesday 01 February 2011, 11:0012:30
Cambridge University
4130
http://sms.cam.ac.uk/media/1095962
A compactification for the moduli stack of bundles on a surface
Baranovsky, V (University of California, Irvine)
Tuesday 01 February 2011, 11:0012:30
We suggest a new moduli functor of quasibundles on a smooth projective surface, which is a stack theoretic counterpart of the Uhlenbeck compactification, and briefly outline its relation with other compactifications constructed by other authors (Balaji, Timofeeva, Schmitt and a few others).
20160601T11:32:24+01:00
4130
1095962
true
16x9
false
no

A new approach for the Toledo invariant
ucs_sms_1087487_1147599
http://sms.cam.ac.uk/media/1147599
A new approach for the Toledo invariant
Biquard, O (Universite Paris 6)
Tuesday 24 May 2011, 10:0011:00
Fri, 03 Jun 2011 14:49:30 +0100
Biquard, O
Steve Greenham
Isaac Newton Institute
Biquard, O
f3c6151036b76c44a392e322ee969b74
39562e663acb134b1bd7415dd91a00db
4da3b9256ae308abcfe22fb61bc657b2
Biquard, O (Universite Paris 6)
Tuesday 24 May 2011, 10:0011:00
Biquard, O (Universite Paris 6)
Tuesday 24 May 2011, 10:0011:00
Cambridge University
4018
http://sms.cam.ac.uk/media/1147599
A new approach for the Toledo invariant
Biquard, O (Universite Paris 6)
Tuesday 24 May 2011, 10:0011:00
I shall explain a new approach for the Toledo invariant from the Higgs bundle point of view, coming from group theoretic properties of Hermitian symmetric spaces. This approach covers all cases uniformly, including the exceptional ones. I shall give some applications. Joint work with O. GarcíaPrada and R. Rubio.
20110603T14:49:39+01:00
4018
1147599
true
16x9
false
no

A set up for the cathegorical Langlands Correspondence
ucs_sms_1087487_1113942
http://sms.cam.ac.uk/media/1113942
A set up for the cathegorical Langlands Correspondence
Pantev, T (Pennsylvania)
Thursday 10 March 2011, 15:3016:30
Fri, 18 Mar 2011 09:42:03 +0000
Pantev, T
Steve Greenham
Isaac Newton Institute
Pantev, T
aab97b4ac4cdaf6e5b57c903af99871f
cf281bfc7756b8cf46c892ba629b6590
43eb747d653e1950554d0c557d9ce9f6
Pantev, T (Pennsylvania)
Thursday 10 March 2011, 15:3016:30
Pantev, T (Pennsylvania)
Thursday 10 March 2011, 15:3016:30
Cambridge University
3864
http://sms.cam.ac.uk/media/1113942
A set up for the cathegorical Langlands Correspondence
Pantev, T (Pennsylvania)
Thursday 10 March 2011, 15:3016:30
20110318T09:42:09+00:00
3864
1113942
true
16x9
false
no

Algebraic approach to tensor product theorems
ucs_sms_1087487_1147648
http://sms.cam.ac.uk/media/1147648
Algebraic approach to tensor product theorems
Balaji, V (Chennai Mathematical Institute)
Thursday 26 May 2011, 11:0012:00
Fri, 03 Jun 2011 15:27:14 +0100
Balaji, V
Steve Greenham
Isaac Newton Institute
Balaji, V
aeae40321231c1157d779f191654df19
fb65b2c0775639079bb07bc93f649098
0474f41eccb01105f652993902ff2fa9
Balaji, V (Chennai Mathematical Institute)
Thursday 26 May 2011, 11:0012:00
Balaji, V (Chennai Mathematical Institute)
Thursday 26 May 2011, 11:0012:00
Cambridge University
4320
http://sms.cam.ac.uk/media/1147648
Algebraic approach to tensor product theorems
Balaji, V (Chennai Mathematical Institute)
Thursday 26 May 2011, 11:0012:00
The aim of the talk is to give the general geometric invariant theoretic approach to proving tensor product theorems of semistable objects as highlighted in the work of Bogomolov and Ramanan & Ramanathan. This approach will be used to give algebraic proofs of the tensor product theorem for semistable Hitchin pairs over arbitrary ground fields. Towards this, one needs to develop a purely algebraic notion of a Hitchin scheme, an object dual in a certain sense to a Hitchin pair.
20110603T15:27:22+01:00
4320
1147648
true
16x9
false
no

Arithmetic and physics of Higgs moduli spaces
ucs_sms_1087487_1154283
http://sms.cam.ac.uk/media/1154283
Arithmetic and physics of Higgs moduli spaces
Hausel, T (Oxford)
Monday 27 June 2011, 10:0011:00
Wed, 29 Jun 2011 15:28:54 +0100
Hausel, T
Steve Greenham
Isaac Newton Institute
Hausel, T
ad71e10215d872398eb9ade462ea2807
031c3d6f05c40f586fffaac5cf9d85a1
c77925c6432d6ac60071e6ef36a37da2
Hausel, T (Oxford)
Monday 27 June 2011, 10:0011:00
Hausel, T (Oxford)
Monday 27 June 2011, 10:0011:00
Cambridge University
4139
http://sms.cam.ac.uk/media/1154283
Arithmetic and physics of Higgs moduli spaces
Hausel, T (Oxford)
Monday 27 June 2011, 10:0011:00
In this talk we discuss the connection between conjectures with Villegas on mixed Hodge polynomials of character varieties of Riemann surfaces achieved by arithmetic means and conjectures on the cohomology of Higgs moduli spaces derived by physicists ChuangDiaconescuPan.
20110629T15:29:02+01:00
4139
1154283
true
16x9
false
no

Augmented bundles  I
ucs_sms_1087487_1087488
http://sms.cam.ac.uk/media/1087488
Augmented bundles  I
Hoffmann, N (Freie Universität Berlin)
Wednesday 05 January 2011, 10:0011:00
Wed, 05 Jan 2011 18:15:28 +0000
Hoffmann, N
Steve Greenham
Isaac Newton Institute
Hoffmann, N
1c66f1acaec887c3cbbb925effa59098
5c24f49edbeaa2c9d510beb4dd6a5153
1aabf19be132475f488896a694592706
Hoffmann, N (Freie Universität Berlin)
Wednesday 05 January 2011, 10:0011:00
Hoffmann, N (Freie Universität Berlin)
Wednesday 05 January 2011, 10:0011:00
Cambridge University
4107
http://sms.cam.ac.uk/media/1087488
Augmented bundles  I
Hoffmann, N (Freie Universität Berlin)
Wednesday 05 January 2011, 10:0011:00
The notion of augmented bundle comprises various extra structures on vector bundles. The lectures deal with examples like quasiparabolic bundles, coherent systems, framed bundles, Higgs bundles, and holomorphic triples, all on a compact Riemann surface. I'll explain their coarse moduli spaces and discuss the role of the stability parameters.
20110105T18:15:33+00:00
4107
1087488
true
16x9
false
no

Augmented bundles  II
ucs_sms_1087487_1087957
http://sms.cam.ac.uk/media/1087957
Augmented bundles  II
Hoffmann, N (Freie Universität Berlin)
Thursday 06 January 2011, 10:0011:00
Thu, 06 Jan 2011 17:15:04 +0000
Hoffmann, N
Steve Greenham
Isaac Newton Institute
Hoffmann, N
221ff158333cb54a4f41fd37f36b2da8
06b24b375fe63ed9f0c780bc9e4c4ac9
a33ac6583f3dfacc87e5b34b6c0b5260
Hoffmann, N (Freie Universität Berlin)
Thursday 06 January 2011, 10:0011:00
Hoffmann, N (Freie Universität Berlin)
Thursday 06 January 2011, 10:0011:00
Cambridge University
4283
http://sms.cam.ac.uk/media/1087957
Augmented bundles  II
Hoffmann, N (Freie Universität Berlin)
Thursday 06 January 2011, 10:0011:00
The notion of augmented bundle comprises various extra structures on vector bundles. The lectures deal with examples like quasiparabolic bundles, coherent systems, framed bundles, Higgs bundles, and holomorphic triples, all on a compact Riemann surface. I'll explain their coarse moduli spaces and discuss the role of the stability parameters.
20110106T17:15:09+00:00
4283
1087957
true
16x9
false
no

bstability and blowups
ucs_sms_1087487_1151898
http://sms.cam.ac.uk/media/1151898
bstability and blowups
Donaldson, S (Imperial)
Thursday 23 June 2011, 15:3016:30
Fri, 24 Jun 2011 17:56:17 +0100
Donaldson, S
Steve Greenham
Isaac Newton Institute
Donaldson, S
d273393beb3da4f1416f5860b24a4fd2
e85cfcf35f5cc985c68456a0a6577031
6beb199917305e765abe9f1d839d73b9
Donaldson, S (Imperial)
Thursday 23 June 2011, 15:3016:30
Donaldson, S (Imperial)
Thursday 23 June 2011, 15:3016:30
Cambridge University
4040
http://sms.cam.ac.uk/media/1151898
bstability and blowups
Donaldson, S (Imperial)
Thursday 23 June 2011, 15:3016:30
In this lecture we will discuss some technical algebrogeometric questions which arise in connection with the existence problem for KahlerEinstein metrics. We will begin by recalling the notion of "bstability", which involves birational transformations of a degeneration. We will then explain how to adapt an argument of Stoppa to make progress towards proving a KahlerEinstein manifold is bstable.
20110624T17:56:25+01:00
4040
1151898
true
16x9
false
no

Birational models of the Hilbert scheme of points on P2 are moduli of Bridgelandstable complexes
ucs_sms_1087487_1147740
http://sms.cam.ac.uk/media/1147740
Birational models of the Hilbert scheme of points on P2 are moduli of Bridgelandstable complexes
Bertram, A (Utah)
Tuesday 31 May 2011, 11:3012:30
Fri, 03 Jun 2011 16:36:54 +0100
Bertram, A
Steve Greenham
Isaac Newton Institute
Bertram, A
751068ef6ac2b735138b57b4e0f971f5
431c00ea920a0f973f87f84481f285e0
09d979731cdfbf96364eaf22c91ee3fd
Bertram, A (Utah)
Tuesday 31 May 2011, 11:3012:30
Bertram, A (Utah)
Tuesday 31 May 2011, 11:3012:30
Cambridge University
4005
http://sms.cam.ac.uk/media/1147740
Birational models of the Hilbert scheme of points on P2 are moduli of Bridgelandstable complexes
Bertram, A (Utah)
Tuesday 31 May 2011, 11:3012:30
The minimal model program applied to the Hilbert scheme of points on P2 yields a series of birational models, followed by a Fano fibration. These birational models are themselves moduli spaces, but not (generally) of sheaves. Rather, they are moduli spaces of Bridgelandstable objects in the derived category. Moreover, each of them may be identified with moduli of quiver representations of the quiver associated to P2 and each wallcrossing is a GIT wallcrossing for a particular representation. This is joint work with Izzet Coskun and Daniele Arcara.
20110603T16:37:02+01:00
4005
1147740
true
16x9
false
no

Bounded cohomology and Higgs bundles
ucs_sms_1087487_1150231
http://sms.cam.ac.uk/media/1150231
Bounded cohomology and Higgs bundles
Ott, A (ETH)
Thursday 16 June 2011, 15:3016:30
Tue, 21 Jun 2011 11:00:12 +0100
Ott, A
Steve Greenham
Isaac Newton Institute
Ott, A
dd93ef932f4d7a57067943c3054f4367
2593ea051df12090daa794481e0d317e
ebdfac12059e2c390caffd89282cfc7d
Ott, A (ETH)
Thursday 16 June 2011, 15:3016:30
Ott, A (ETH)
Thursday 16 June 2011, 15:3016:30
Cambridge University
4035
http://sms.cam.ac.uk/media/1150231
Bounded cohomology and Higgs bundles
Ott, A (ETH)
Thursday 16 June 2011, 15:3016:30
Over the past several years, representations of fundamental groups of compact complex hyperbolic manifolds into Hermitian Lie groups have been studied using bounded group cohomology on the one hand and Higgs bundles on the other hand. In this talk, we will discuss some aspects of the interplay between these two approaches. This is joint work with Tobias Hartnick.
20110621T11:00:21+01:00
4035
1150231
true
16x9
false
no

BPS states, DonaldsonThomas invariants and Hitchin pairs
ucs_sms_1087487_1132238
http://sms.cam.ac.uk/media/1132238
BPS states, DonaldsonThomas invariants and Hitchin pairs
Diaconescu, DE (Rutgers)
Thursday 14 April 2011, 11:3012:30
Mon, 18 Apr 2011 11:29:28 +0100
Diaconescu, DE
Steve Greenham
Isaac Newton Institute
Diaconescu, DE
ad15ee712af7069b9a07cda0db4134b3
85097a29722ec084c0196a35da894289
21e4e222cbd0982fcb1d53be9d3c290d
Diaconescu, DE (Rutgers)
Thursday 14 April 2011, 11:3012:30
Diaconescu, DE (Rutgers)
Thursday 14 April 2011, 11:3012:30
Cambridge University
3302
http://sms.cam.ac.uk/media/1132238
BPS states, DonaldsonThomas invariants and Hitchin pairs
Diaconescu, DE (Rutgers)
Thursday 14 April 2011, 11:3012:30
A string theoretic construction will be presented relating BPS states, DonaldsonThomas invariants and the cohomology of the Hitchin system. In particular, the work of Hausel and RodrgiguezVillegas will be given a natural physical explanation based on geometric engineering.
This is work in collaboration with Wuyen Chuang and Guang Pan.
20110418T11:29:36+01:00
3302
1132238
true
16x9
false
no

Bridgeland stability conditions and FourierMukai transforms
ucs_sms_1087487_1154960
http://sms.cam.ac.uk/media/1154960
Bridgeland stability conditions and FourierMukai transforms
Yoshioka, K (Kobe)
Thursday 30 June 2011, 16:3017:30
Fri, 01 Jul 2011 16:43:27 +0100
Yoshioka, K
Steve Greenham
Isaac Newton Institute
Yoshioka, K
f2637c91d69ae2e224c1734d058c48a7
cb6d9d66a956c5c16e464009b48bcf3a
d8d29139b422e42f75e5602f4205869e
Yoshioka, K (Kobe)
Thursday 30 June 2011, 16:3017:30
Yoshioka, K (Kobe)
Thursday 30 June 2011, 16:3017:30
Cambridge University
3792
http://sms.cam.ac.uk/media/1154960
Bridgeland stability conditions and FourierMukai transforms
Yoshioka, K (Kobe)
Thursday 30 June 2011, 16:3017:30
Bridgeland stability condition is preserved under the FourierMukai transform by its definition. I will explain the relation with Gieseker stability. In particular, I will explain kown results on the birational maps of moduli spaces by using Bridgeland stability condition.
20110701T16:43:36+01:00
3792
1154960
true
16x9
false
no

Bridgeland stability conditions on threefolds and birational geometry
ucs_sms_1087487_1126477
http://sms.cam.ac.uk/media/1126477
Bridgeland stability conditions on threefolds and birational geometry
Bayer, A (Connecticut)
Monday 04 April 2011, 14:0015:00
Mon, 11 Apr 2011 11:07:28 +0100
Bayer, A
Steve Greenham
Isaac Newton Institute
Bayer, A
58432366005c50dce41b140f73334ae0
54c90f47cb5456f799ff65cf1fa049f4
2595701048b0941213e4d6f15d0e1713
Bayer, A (Connecticut)
Monday 04 April 2011, 14:0015:00
Bayer, A (Connecticut)
Monday 04 April 2011, 14:0015:00
Cambridge University
3566
http://sms.cam.ac.uk/media/1126477
Bridgeland stability conditions on threefolds and birational geometry
Bayer, A (Connecticut)
Monday 04 April 2011, 14:0015:00
I will explain a conjectural construction of Bridgeland stability conditions on smooth projective threefolds. It is based on a construction of new tstructures. They produce a stability condition if we assume a conjectural BogomolovGieseker type inequality for the Chern character of certain stable complexes. In this talk, I will present evidence for our conjecture, as well as implications of the conjecture to the birational geometry of threefolds. In particular, it implies a weaker version of Fujita's conjecture. This is based on joint work with Aaron Bertram, Emanuele Macrì and Yukinobu Toda.
20110411T11:07:35+01:00
3566
1126477
true
16x9
false
no

BrillNoether theory for vector bundles with fixed determinant
ucs_sms_1087487_1154456
http://sms.cam.ac.uk/media/1154456
BrillNoether theory for vector bundles with fixed determinant
Teixidor i Bigas, M (Tufts)
Tuesday 28 June 2011, 11:3012:30
Wed, 29 Jun 2011 17:02:04 +0100
Teixidor i Bigas, M
Steve Greenham
Isaac Newton Institute
Teixidor i Bigas, M
b0af8ce0e0f1169baff719538e8a8e3e
a3b87101dea75a7a4043582a8c539fdc
c3fc4a0c3d712014045b94a2d44cc357
Teixidor i Bigas, M (Tufts)
Tuesday 28 June 2011, 11:3012:30
Teixidor i Bigas, M (Tufts)
Tuesday 28 June 2011, 11:3012:30
Cambridge University
3363
http://sms.cam.ac.uk/media/1154456
BrillNoether theory for vector bundles with fixed determinant
Teixidor i Bigas, M (Tufts)
Tuesday 28 June 2011, 11:3012:30
Consider the set of vector bundles or rank r and fixed determinant L with at least k sections. The case of rank two and L canonical has been studied for a few years and some conjectures of Bertram Feinberg and Mukai are by now mostly proved. We will discuss some partial results for other determinants, mostly for rank two.
20110629T17:02:13+01:00
3363
1154456
true
16x9
false
no

Bundles of rank 2 with 4 sections on curves
ucs_sms_1087487_1150177
http://sms.cam.ac.uk/media/1150177
Bundles of rank 2 with 4 sections on curves
Grzegorczyk, I (CSUCI)
Tuesday 14 June 2011, 11:3012:30
Tue, 21 Jun 2011 08:34:52 +0100
Grzegorczyk, I
Steve Greenham
Isaac Newton Institute
Grzegorczyk, I
aae35692c50a565cc6a403a212c74d7c
0c6890c40e64b2d05fba669ef975459d
11df83a4d002943f4c8ffb0bcc1b36b6
Grzegorczyk, I (CSUCI)
Tuesday 14 June 2011, 11:3012:30
Grzegorczyk, I (CSUCI)
Tuesday 14 June 2011, 11:3012:30
Cambridge University
3316
http://sms.cam.ac.uk/media/1150177
Bundles of rank 2 with 4 sections on curves
Grzegorczyk, I (CSUCI)
Tuesday 14 June 2011, 11:3012:30
We study stable bundles with 4 sections on a smooth algebraic curve. We give geometric constructions for such bundles of lowest possible degree on curves of genus 10 and interpret the results in terms of generalized Clifford indices. We report on related examples and the current situations for rank 2 BrillNoether theory.
20110621T08:35:01+01:00
3316
1150177
true
16x9
false
no

Calculating Thom polynomials
ucs_sms_1087487_1105262
http://sms.cam.ac.uk/media/1105262
Calculating Thom polynomials
Szenes, A (Genève)
Tuesday 01 March 2011, 10:0011:00
Fri, 04 Mar 2011 10:43:41 +0000
Szenes, A
Steve Greenham
Isaac Newton Institute
Szenes, A
ee26651874b1febd3b6b27511c71538b
05213d13620cd59f0daf133ae486ee50
24ef2ad5263ee47719f4d2869faef261
Szenes, A (Genève)
Tuesday 01 March 2011, 10:0011:00
Szenes, A (Genève)
Tuesday 01 March 2011, 10:0011:00
Cambridge University
4003
http://sms.cam.ac.uk/media/1105262
Calculating Thom polynomials
Szenes, A (Genève)
Tuesday 01 March 2011, 10:0011:00
There is a polynomial invariant, introduced by Thom in the 1950s, which links the enumerative characteristics of manifolds with the type of singularities which cannot be avoided in maps between them. In this talk, I will report on recent progress in calculating these polynomials.
20110304T10:43:46+00:00
4003
1105262
true
16x9
false
no

Categorical Matrix Factorizations
ucs_sms_1087487_1132170
http://sms.cam.ac.uk/media/1132170
Categorical Matrix Factorizations
Horja, P (Oklahoma State)
Wednesday 13 April 2011, 10:0011:00
Mon, 18 Apr 2011 10:34:31 +0100
Horja, P
Steve Greenham
Isaac Newton Institute
Horja, P
aacb1ab03807b74dc760bf5c3dfcc075
dbcba21cd2579029d1c8cdd0afce09ee
1dc8b75801bad957a1a59f1a5e364dcf
Horja, P (Oklahoma State)
Wednesday 13 April 2011, 10:0011:00
Horja, P (Oklahoma State)
Wednesday 13 April 2011, 10:0011:00
Cambridge University
4086
http://sms.cam.ac.uk/media/1132170
Categorical Matrix Factorizations
Horja, P (Oklahoma State)
Wednesday 13 April 2011, 10:0011:00
I will present a notion of matrix factorizations associated to an additive category endowed with a weak action of the integers. The role of the potential is played by a certain natural transformation compatible with the categorical weak action. Various applications of this framework to the understanding of LandauGinzburg models will be explored.
20110418T10:34:38+01:00
4086
1132170
true
16x9
false
no

Categorified Heisenberg actions on Hilbert schemes
ucs_sms_1087487_1131583
http://sms.cam.ac.uk/media/1131583
Categorified Heisenberg actions on Hilbert schemes
Cautis, S (Columbia, NY)
Monday 11 April 2011, 11:3012:30
Fri, 15 Apr 2011 12:49:26 +0100
Cautis, S
Steve Greenham
Isaac Newton Institute
Cautis, S
4febc8c2491551cabfdc3a091feb4cd1
0c6591714602e9a05876766bd3466efe
a6500207006eca3ebb665c220dc75880
Cautis, S (Columbia, NY)
Monday 11 April 2011, 11:3012:30
Cautis, S (Columbia, NY)
Monday 11 April 2011, 11:3012:30
Cambridge University
3657
http://sms.cam.ac.uk/media/1131583
Categorified Heisenberg actions on Hilbert schemes
Cautis, S (Columbia, NY)
Monday 11 April 2011, 11:3012:30
I will describe an action of a quantized Heisenberg algebra on the (derived) categories of coherent sheaves on Hilbert schemes of ALE spaces (crepant resolutions of C^2/G). This action essentially lifts the actions of Nakajima and Grojnowski on the cohomology of these spaces. (joint with Tony Licata)
20110415T12:49:33+01:00
3657
1131583
true
16x9
false
no

Cell decompositions of moduli spaces and generalisations
ucs_sms_1087487_1095981
http://sms.cam.ac.uk/media/1095981
Cell decompositions of moduli spaces and generalisations
Giansiracusa, JH (University of Bath)
Thursday 03 February 2011, 14:0015:00
Tue, 08 Feb 2011 14:08:57 +0000
Giansiracusa, JH
Steve Greenham
Isaac Newton Institute
Giansiracusa, JH
32aadbd6a9769a5e870f9de068e5a4f0
451069d90e7d613df030acdaa52e8685
cb8c211f00a0563b9773b7d51bbb4013
Giansiracusa, JH (University of Bath)
Thursday 03 February 2011, 14:0015:00
Giansiracusa, JH (University of Bath)
Thursday 03 February 2011, 14:0015:00
Cambridge University
3451
http://sms.cam.ac.uk/media/1095981
Cell decompositions of moduli spaces and generalisations
Giansiracusa, JH (University of Bath)
Thursday 03 February 2011, 14:0015:00
20110208T14:09:02+00:00
3451
1095981
true
16x9
false
no

Compactifications of reductive groups as moduli stacks of bundles
ucs_sms_1087487_1154394
http://sms.cam.ac.uk/media/1154394
Compactifications of reductive groups as moduli stacks of bundles
Martens, J (Aarhus)
Monday 27 June 2011, 15:2015:50
Wed, 29 Jun 2011 16:25:06 +0100
Martens, J
Steve Greenham
Isaac Newton Institute
Martens, J
feb434fc8cb6a65558983e9cac819c69
b80c1c344f7e4242b800f04f39039429
56bd753063a797ac94724fc008a51ea2
Martens, J (Aarhus)
Monday 27 June 2011, 15:2015:50
Martens, J (Aarhus)
Monday 27 June 2011, 15:2015:50
Cambridge University
2160
http://sms.cam.ac.uk/media/1154394
Compactifications of reductive groups as moduli stacks of bundles
Martens, J (Aarhus)
Monday 27 June 2011, 15:2015:50
Given a reductive group G, we introduce a class of moduli problems of framed principal Gbundles on chains of projective lines. Their moduli stacks provide equivariant toroidal compactifications of G. All toric orbifolds are examples of this construction, as are the wonderful compactifications of adjoint groups of De ConciniProcesi. As an additional benefit, we show that every semisimple group has a canonical orbifold compactification. We further indicate the connection with nonabelian symplectic cutting and the LosevManin spaces. This is joint work with Michael Thaddeus (Columbia U).
20110629T16:25:14+01:00
2160
1154394
true
16x9
false
no

Counterexamples of high Clifford index to PrymTorelli
ucs_sms_1087487_1097462
http://sms.cam.ac.uk/media/1097462
Counterexamples of high Clifford index to PrymTorelli
Izadi, E (Georgia)
Tuesday 08 February 2011, 11:3012:30
Mon, 14 Feb 2011 12:30:52 +0000
Izadi, E
Steve Greenham
Isaac Newton Institute
Izadi, E
6e2fe8c87af58f1b6b603b4e30a65214
4085bd429ad832dc7ea9113de6f17df5
f7dd9c4c5a0fac89f48677067edda61b
Izadi, E (Georgia)
Tuesday 08 February 2011, 11:3012:30
Izadi, E (Georgia)
Tuesday 08 February 2011, 11:3012:30
Cambridge University
3526
http://sms.cam.ac.uk/media/1097462
Counterexamples of high Clifford index to PrymTorelli
Izadi, E (Georgia)
Tuesday 08 February 2011, 11:3012:30
For an \'etale double cover of smooth curves, the Prym variety is essentially the ``difference'' between the jacobians of the two curves. The Torelli problem for the Prym map asks when two double covers have the same Prym variety. It is known that the Prym map from the moduli space of double covers of curves of genus g at least 7 to principally polarized abelian varieties of dimension g1 is generically injective. Counterexamples to the injectivity of the Prym map were, up to now, given by Donagi's tetragonal construction and by Verra's construction for plane sextics. It was conjectured that all counterexamples are obtained from double covers of curves of Clifford index at most 3. I will discuss counterexamples to this conjecture constructed by myself and Herbert Lange.
20110214T12:30:58+00:00
3526
1097462
true
16x9
false
no

Coupled equations for Kähler metrics and YangMills connections
ucs_sms_1087487_1150159
http://sms.cam.ac.uk/media/1150159
Coupled equations for Kähler metrics and YangMills connections
AlvarezConsul, L (ICMAT)
Tuesday 14 June 2011, 10:0011:00
Tue, 21 Jun 2011 08:16:07 +0100
AlvarezConsul, L
Steve Greenham
Isaac Newton Institute
AlvarezConsul, L
7a1a9c24eae7dcf5ed3c179a681d1be0
f3f4bcc1adc26fd9ffa587497f3d1c4a
c3d3a28b7dd106768f4b1de9a602afdb
AlvarezConsul, L (ICMAT)
Tuesday 14 June 2011, 10:0011:00
AlvarezConsul, L (ICMAT)
Tuesday 14 June 2011, 10:0011:00
Cambridge University
3667
http://sms.cam.ac.uk/media/1150159
Coupled equations for Kähler metrics and YangMills connections
AlvarezConsul, L (ICMAT)
Tuesday 14 June 2011, 10:0011:00
We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kähler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kähler metric and HermiteYangMills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, the Mabuchi Kenergy and geodesic stability. We finish by giving some examples of solutions. This is joint work with Mario GarciaFernandez and Oscar GarciaPrada (arXiv:1102.0991 [math.DG]).
20110621T08:16:16+01:00
3667
1150159
true
16x9
false
no

Coupled Equations, cscK metrics and geodesic stability
ucs_sms_1087487_1094281
http://sms.cam.ac.uk/media/1094281
Coupled Equations, cscK metrics and geodesic stability
GarciaFernandez, M (Aarhus Universitet)
Thursday 27 January 2011, 14:0015:00
Mon, 31 Jan 2011 09:18:55 +0000
GarciaFernandez, M
Steve Greenham
Isaac Newton Institute
GarciaFernandez, M
18765588ffbf57e680609e6b8b09606e
c6ac78c10821f569088a53db5e60d69b
b40e6b4886ceb858131df37c1bb41df3
GarciaFernandez, M (Aarhus Universitet)
Thursday 27 January 2011, 14:0015:00
GarciaFernandez, M (Aarhus Universitet)
Thursday 27 January 2011, 14:0015:00
Cambridge University
3718
http://sms.cam.ac.uk/media/1094281
Coupled Equations, cscK metrics and geodesic stability
GarciaFernandez, M (Aarhus Universitet)
Thursday 27 January 2011, 14:0015:00
We introduce a system of partial differential equations coupling a Kähler metric on a compact complex manifold X and a connection on a principal bundle over X. These equations generalize the constant scalar curvature equation for a Kähler metric on a complex manifold and the HermitianYangMills equations for a connection on a bundle. They have an interpretation in terms of a moment map, where the group of symmetries is an extension of the gauge group of the bundle that moves the base X. We develop a natural "formal picture" for the problem which leads to analytic obstructions for the existence of solutions. When the structure group of the bundle is trivial we recover known obstructions for the theory of cscK metrics, in particular the Futaki invariant and the notion of geodesic stability. This is joint work with Luis Alvarez Consul and Oscar Garcia Prada.
20110131T09:19:01+00:00
3718
1094281
true
16x9
false
no

Curve counting invariants on CalabiYau 3folds
ucs_sms_1087487_1137382
http://sms.cam.ac.uk/media/1137382
Curve counting invariants on CalabiYau 3folds
Toda, Y (IPMU, Japan)
Thursday 05 May 2011, 15:1516:15
Spitalfields Day
Fri, 06 May 2011 11:39:52 +0100
Toda, Y
Steve Greenham
Isaac Newton Institute
Toda, Y
57c9fa74b57a9f4e03f224cdd294e3b7
e10ccf98c5d711fcc9d448696cd7bb38
3b51f5fbf51381bb089fe9a030dd7fc8
Toda, Y (IPMU, Japan)
Thursday 05 May 2011, 15:1516:15
Spitalfields Day
Toda, Y (IPMU, Japan)
Thursday 05 May 2011, 15:1516:15
Spitalfields Day
Cambridge University
3745
http://sms.cam.ac.uk/media/1137382
Curve counting invariants on CalabiYau 3folds
Toda, Y (IPMU, Japan)
Thursday 05 May 2011, 15:1516:15
Spitalfields Day
I give an introduction of DonaldsonThomas type curve counting invariants on CalabiYau 3folds, and explain the recent developments.
20110506T11:40:00+01:00
3745
1137382
true
16x9
false
no

Dmanifolds, a new theory of derived differential geometry
ucs_sms_1087487_1132264
http://sms.cam.ac.uk/media/1132264
Dmanifolds, a new theory of derived differential geometry
Joyce, D (Oxford)
Thursday 14 April 2011, 16:3017:30
Mon, 18 Apr 2011 11:49:47 +0100
Joyce, D
Steve Greenham
Isaac Newton Institute
Joyce, D
cdc10a19d705a63b6dbc426547f76a0c
202c06f78d4012e662079bd54551485e
fe8e69d7ab5fb0ac20eef03bbcc23794
Joyce, D (Oxford)
Thursday 14 April 2011, 16:3017:30
Joyce, D (Oxford)
Thursday 14 April 2011, 16:3017:30
Cambridge University
3875
http://sms.cam.ac.uk/media/1132264
Dmanifolds, a new theory of derived differential geometry
Joyce, D (Oxford)
Thursday 14 April 2011, 16:3017:30
I describe a new class of geometric objects I call "dmanifolds". Dmanifolds are a kind of "derived" smooth manifold, where "derived" is in the sense of the derived algebraic geometry of Jacob Lurie, Bertrand Toen, etc. The definition draws on ideas of Jacob Lurie, David Spivak. The original aim of the project, which I believe I have achieved, is to find the "right" definition of the Kuranishi spaces of Fukaya, Oh, Ohta and Ono, which is the geometric structure on moduli spaces of Jholomorphic curves in a symplectic manifold.
The definition of dmanifolds involves doing algebraic geometry over smooth functions (Cinfinity rings); roughly speaking, a dmanifold is a differentialgeometric analogue of a scheme with a perfect obstruction theory. Dmanifolds form a strict 2category dMan. It is a 2subcategory of the larger 2category of "dspaces" dSpa. The definition does not involve localization of categories, so we have very good control of what 1morphisms and 2morphisms are.
The 2categories dMan and dSpa have some very nice properties. All fibre products exist in dSpa, and a fibre product of dmanifolds is a dmanifold under weak transversality condition. For example, any fibre product of two dmanifolds over a manifold is a dmanifold. You can glue dmanifolds by equivalences of open dsubmanifolds (a kind of pushout in dMan) provided the glued topological space is Hausdorff. There is a notion of "virtual cotangent bundle" of a dmanifold, which lives in a 2category of virtual vector bundles, and a 1morphism of dmanifolds is etale (a local equivalence) iff it induces an equivalence of virtual cotangent bundles. And so on.
There are also good notions of dmanifolds with boundary and dmanifolds with corners, and orbifold versions of all this, dorbifolds.
Dmanifolds and dorbifolds have applications to moduli spaces and enumerative invariants in both differential and algebraic geometry. Almost any moduli space which is used to define some kind of counting invariant should have a dmanifold or dorbifold structure. Any moduli space of solutions of a smooth nonlinear elliptic p.d.e. on a compact manifold has a dmanifold structure. Any Cscheme with a perfect obstruction theory has a dmanifold structure. In symplectic geometry, Kuranishi spaces and polyfold structures on moduli spaces of Jholomorphic curves induce dorbifold structures. So much of GromovWitten theory, DonaldsonThomas theory, Lagrangian Floer cohomology, Symplectic Field Theory,... can be rewritten in this language.
20110418T11:49:56+01:00
3875
1132264
true
16x9
false
no

Deformation Theory : an introduction to the algebraic approach  I
ucs_sms_1087487_1087651
http://sms.cam.ac.uk/media/1087651
Deformation Theory : an introduction to the algebraic approach  I
Nitsure, N (Tata Institute of Fundamental Research)
Wednesday 05 January 2011, 15:3016:30
Thu, 06 Jan 2011 10:04:28 +0000
Nitsure, N
Steve Greenham
Isaac Newton Institute
Nitsure, N
c0de15312a47e0ef2ffa9209971d1bf6
9eecbc471a658cf3622f7334382da8cf
0974659c01a86d73e59bb1f6f1c043fe
Nitsure, N (Tata Institute of Fundamental Research)
Wednesday 05 January 2011,...
Nitsure, N (Tata Institute of Fundamental Research)
Wednesday 05 January 2011, 15:3016:30
Cambridge University
4250
http://sms.cam.ac.uk/media/1087651
Deformation Theory : an introduction to the algebraic approach  I
Nitsure, N (Tata Institute of Fundamental Research)
Wednesday 05 January 2011, 15:3016:30
This series of three lectures aims to give an introduction to the algebraic approach to deformation theory, as developed by Grothendieck, Schlessinger, Illusie and Artin, illustrated with a few key examples.
The topics will include (i) infinitesimal theory over Artin local rings including Schlessinger's theorem, tangentobstruction theories and use of cotangent complex, (ii) algebraization via the Grothendieck existence theorem for formal schemes and the Artin approximation theorem, and (iii) construction of global moduli as quotient algebraic spaces.
20110106T10:04:33+00:00
4250
1087651
true
16x9
false
no

Deformation Theory : an introduction to the algebraic approach  II
ucs_sms_1087487_1088090
http://sms.cam.ac.uk/media/1088090
Deformation Theory : an introduction to the algebraic approach  II
Nitsure, N (Tata Institute of Fundamental Research)
Thursday 06 January 2011, 15:3016:30
Thu, 06 Jan 2011 17:54:40 +0000
Nitsure, N
Steve Greenham
Isaac Newton Institute
Nitsure, N
4c4624a35cc84fd812af7e6971bb2e85
7db68079d3ac1b7628fdf891a95895b8
bce671620deadaebd48e69a55d61121a
Nitsure, N (Tata Institute of Fundamental Research)
Thursday 06 January 2011,...
Nitsure, N (Tata Institute of Fundamental Research)
Thursday 06 January 2011, 15:3016:30
Cambridge University
4883
http://sms.cam.ac.uk/media/1088090
Deformation Theory : an introduction to the algebraic approach  II
Nitsure, N (Tata Institute of Fundamental Research)
Thursday 06 January 2011, 15:3016:30
This series of three lectures aims to give an introduction to the algebraic approach to deformation theory, as developed by Grothendieck, Schlessinger, Illusie and Artin, illustrated with a few key examples.
The topics will include (i) infinitesimal theory over Artin local rings including Schlessinger's theorem, tangentobstruction theories and use of cotangent complex, (ii) algebraization via the Grothendieck existence theorem for formal schemes and the Artin approximation theorem, and (iii) construction of global moduli as quotient algebraic spaces.
20110106T17:54:45+00:00
4883
1088090
true
16x9
false
no

Deformation Theory : an introduction to the algebraic approach  III
ucs_sms_1087487_1088878
http://sms.cam.ac.uk/media/1088878
Deformation Theory : an introduction to the algebraic approach  III
Nitsure, N (Tata Institute of Fundamental Research)
Friday 07 January 2011, 15:3016:30
Mon, 10 Jan 2011 13:43:42 +0000
Nitsure, N
Steve Greenham
Isaac Newton Institute
Nitsure, N
1bbc104906d9c4f0b346415d7c758dae
7069dc783c4f918c1bf308b305264342
22dfc915194f236474f0f04a09de3d2b
Nitsure, N (Tata Institute of Fundamental Research)
Friday 07 January 2011,...
Nitsure, N (Tata Institute of Fundamental Research)
Friday 07 January 2011, 15:3016:30
Cambridge University
3663
http://sms.cam.ac.uk/media/1088878
Deformation Theory : an introduction to the algebraic approach  III
Nitsure, N (Tata Institute of Fundamental Research)
Friday 07 January 2011, 15:3016:30
This series of three lectures aims to give an introduction to the algebraic approach to deformation theory, as developed by Grothendieck, Schlessinger, Illusie and Artin, illustrated with a few key examples.
The topics will include (i) infinitesimal theory over Artin local rings including Schlessinger's theorem, tangentobstruction theories and use of cotangent complex, (ii) algebraization via the Grothendieck existence theorem for formal schemes and the Artin approximation theorem, and (iii) construction of global moduli as quotient algebraic spaces.
20110111T17:33:03+00:00
3663
1088878
true
16x9
false
no

DeligneHodge polynomials for SL(2,C)character varieties of genus 1 and 2.
ucs_sms_1087487_1154942
http://sms.cam.ac.uk/media/1154942
DeligneHodge polynomials for SL(2,C)character varieties of genus 1 and 2.
Logares, M (ICMAT)
Thursday 30 June 2011, 15:2015:50
Fri, 01 Jul 2011 16:30:54 +0100
Logares, M
Steve Greenham
Isaac Newton Institute
Logares, M
502713db7c3ffee6e8926ea1e68f5290
ea95b8c1d38e4b71c875d76c3b6c9fc3
a11136f4626f848d1e2111af7a7bcf26
Logares, M (ICMAT)
Thursday 30 June 2011, 15:2015:50
Logares, M (ICMAT)
Thursday 30 June 2011, 15:2015:50
Cambridge University
1783
http://sms.cam.ac.uk/media/1154942
DeligneHodge polynomials for SL(2,C)character varieties of genus 1 and 2.
Logares, M (ICMAT)
Thursday 30 June 2011, 15:2015:50
We give a method to compute DeligneHodge polinomials for various SL(2,C)character varieties, with fixed conjugacy classes equal to Id, Id, diagonal and Jordan type matrices. We will split them into suitable stratifications and analyze the behaviour of the polynomial for them. This is joint work with V. Mu~noz and P. Newstead.
20110701T16:31:03+01:00
1783
1154942
true
16x9
false
no

Derived categories and rationality of conic bundles
ucs_sms_1087487_1154902
http://sms.cam.ac.uk/media/1154902
Derived categories and rationality of conic bundles
Bolognesi, M (Rennes 1)
Thursday 30 June 2011, 14:0014:30
Fri, 01 Jul 2011 16:02:02 +0100
Bolognesi, M
Steve Greenham
Isaac Newton Institute
Bolognesi, M
fcc45962fb5de677310dff4df0bd8e43
1505b9bb5a20310714ed30494e190000
4b23fbc48795bae48368f390139bdf4c
Bolognesi, M (Rennes 1)
Thursday 30 June 2011, 14:0014:30
Bolognesi, M (Rennes 1)
Thursday 30 June 2011, 14:0014:30
Cambridge University
1616
http://sms.cam.ac.uk/media/1154902
Derived categories and rationality of conic bundles
Bolognesi, M (Rennes 1)
Thursday 30 June 2011, 14:0014:30
In this talk I present a joint work with Marcello Bernardara where we show that a standard conic bundle on a rational minimal surface is rational if and only if its derived category admits a semiothogonal decomposition via derived categories of smooth projective curves and exceptional objects. In particular, even if the surface is not minimal, such a decomposition allows to reconstruct the intermediate Jacobian as the direct sum of the Jacobian of those curves.
20110701T16:02:11+01:00
1616
1154902
true
16x9
false
no

Derived equivalences of Azumaya algebras on K3 surfaces
ucs_sms_1087487_1154922
http://sms.cam.ac.uk/media/1154922
Derived equivalences of Azumaya algebras on K3 surfaces
Khalid, M (St. Patrick's College Drumcondra)
Thursday 30 June 2011, 14:4015:10
Fri, 01 Jul 2011 16:23:22 +0100
Khalid, M
Steve Greenham
Isaac Newton Institute
Khalid, M
fa57ec58c8748f4de17e19823690fd80
fef78ae733679fda06f106951e39285a
a4faf9fc39cfb4f8c275ff9eb1194288
Khalid, M (St. Patrick's College Drumcondra)
Thursday 30 June 2011, 14:4015:10
Khalid, M (St. Patrick's College Drumcondra)
Thursday 30 June 2011, 14:4015:10
Cambridge University
1829
http://sms.cam.ac.uk/media/1154922
Derived equivalences of Azumaya algebras on K3 surfaces
Khalid, M (St. Patrick's College Drumcondra)
Thursday 30 June 2011, 14:4015:10
We consider moduli spaces of Azumaya algebras on K3 surfaces. These correspond to twisted sheaves. We prove that when _(A) is zero and c2(A) is within 2r of its minimal bound, where r2 is the rank of A, then the moduli space if non empty is a smooth projective surface. We construct a moduli space of Azumaya algebras on the double cover of the projective plane. In some other special cases we prove a derived equivalence between K3 surfaces and moduli spaces of Azumaya algebras.
20110701T16:23:31+01:00
1829
1154922
true
16x9
false
no

Derived McKay correspondence in dimensions 4 and above
ucs_sms_1087487_1093867
http://sms.cam.ac.uk/media/1093867
Derived McKay correspondence in dimensions 4 and above
Logvinenko, T (Warwick)
Tuesday 18 January 2011, 11:3012:30
Thu, 27 Jan 2011 12:13:51 +0000
Logvinenko, T
Steve Greenham
Isaac Newton Institute
Logvinenko, T
9778e639b76f43320a99c779e71608d6
e0a2bb4fc6e3635adc1b5b41753e6924
2952c07b7dc019908012439088a3f17f
Logvinenko, T (Warwick)
Tuesday 18 January 2011, 11:3012:30
Logvinenko, T (Warwick)
Tuesday 18 January 2011, 11:3012:30
Cambridge University
4537
http://sms.cam.ac.uk/media/1093867
Derived McKay correspondence in dimensions 4 and above
Logvinenko, T (Warwick)
Tuesday 18 January 2011, 11:3012:30
Given a finite subgroup G of SL_n(C) the McKay correspondence studies the relation between Gequivalent geometry of C^n and the geometry of a resolution of Y of C^n/G. In their groundbreaking work, Bridgeland, Kind, and Reid have established that for n = 2,3 the scheme Y = GHilb(C^n) is a crepant resolution of C^n/G and that the derived category D(Y) is equivalent to the Gequivalent derived category D^G(C^n). It follows that we also have D(Y) = D^G(C^3) for any other crepant resolution Y of C^3/G. In this talk, I discuss possible ways of generalizing this to dimension 4 and above.
20110127T12:13:57+00:00
4537
1093867
true
16x9
false
no

Exceptional collections on Grassmannians of classical groups
ucs_sms_1087487_1132189
http://sms.cam.ac.uk/media/1132189
Exceptional collections on Grassmannians of classical groups
Kuznetsov, A (RAS)
Wednesday 13 April 2011, 15:0016:00
Mon, 18 Apr 2011 10:50:32 +0100
Kuznetsov, A
Steve Greenham
Isaac Newton Institute
Kuznetsov, A
515fefbe77a0ec742d345027704c8bd6
21ed430de545ad32cf09944b7a400303
bc919a8033a1a185247d06ae65819677
Kuznetsov, A (RAS)
Wednesday 13 April 2011, 15:0016:00
Kuznetsov, A (RAS)
Wednesday 13 April 2011, 15:0016:00
Cambridge University
4271
http://sms.cam.ac.uk/media/1132189
Exceptional collections on Grassmannians of classical groups
Kuznetsov, A (RAS)
Wednesday 13 April 2011, 15:0016:00
I will describe a new approach to construction of exceptional collections on homogeneous varieties of semisimple algebraic groups. Using this approach I will construct exceptional collections of the expected length on all Grassmannians of classical groups. This is a joint work with Sasha Polishchuk.
20110418T10:50:39+01:00
4271
1132189
true
16x9
false
no

Extensions of Grothendieck's theorem on principal bundles over the projective line
ucs_sms_1087487_1151861
http://sms.cam.ac.uk/media/1151861
Extensions of Grothendieck's theorem on principal bundles over the projective line
Thaddeus, M (Columbia)
Tuesday 21 June 2011, 11:3012:30
Fri, 24 Jun 2011 16:17:29 +0100
Thaddeus, M
Steve Greenham
Isaac Newton Institute
Thaddeus, M
942b7906dadf6844abd45daec845ad9f
3922094199687cfa588526f9899521a9
36f6213494883e26bb97c519a4c366b1
79391606e017e12c8185ee0eca88b1d4
6538c587507a898a6ec0683310f2e4db
Thaddeus, M (Columbia)
Tuesday 21 June 2011, 11:3012:30
Thaddeus, M (Columbia)
Tuesday 21 June 2011, 11:3012:30
Cambridge University
3887
http://sms.cam.ac.uk/media/1151861
Extensions of Grothendieck's theorem on principal bundles over the projective line
Thaddeus, M (Columbia)
Tuesday 21 June 2011, 11:3012:30
Let G be a split reductive group over a field. Grothendieck and Harder proved that any principal Gbundle over the projective line reduces (essentially uniquely) to a maximal torus. In joint work with Johan Martens, we show that this remains true when the base is a chain of lines, a football, a chain of footballs, a finite abelian gerbe over any of these, or the stacktheoretic quotient of any of these by a torus action.
20110624T16:17:38+01:00
3887
1151861
true
4x3
false
no

Further Examples of Bridgeland Stable Moduli Spaces
ucs_sms_1087487_1151889
http://sms.cam.ac.uk/media/1151889
Further Examples of Bridgeland Stable Moduli Spaces
Maciocia, A (Edinburgh)
Thursday 23 June 2011, 14:0015:00
Fri, 24 Jun 2011 18:02:10 +0100
Maciocia, A
Steve Greenham
Isaac Newton Institute
Maciocia, A
ab98e7e27c16cc680a4c878a614e0a21
bc15d366228708cab8c9fd4b0d6a940c
c49a1866704c4597da8e17b6fba2cb96
3af6f80636d54833302937da97602e26
3e774502f03499aee073d08a1248e68f
Maciocia, A (Edinburgh)
Thursday 23 June 2011, 14:0015:00
Maciocia, A (Edinburgh)
Thursday 23 June 2011, 14:0015:00
Cambridge University
3427
http://sms.cam.ac.uk/media/1151889
Further Examples of Bridgeland Stable Moduli Spaces
Maciocia, A (Edinburgh)
Thursday 23 June 2011, 14:0015:00
Following recent work of Arcara and Bertram who give explicit constructions of moduli spaces of certain zero rank Bridgeland stable objects in the derived category of a surface with zero canonical class, we give a complete description of the Bridgeland stable objects with rank 1 and first Chern class equal to twice the polarization on an irreducible principally polarized abelian surface.
20110624T18:02:19+01:00
3427
1151889
true
4x3
false
no

Generalisation of the tetragonal construction
ucs_sms_1087487_1137296
http://sms.cam.ac.uk/media/1137296
Generalisation of the tetragonal construction
Lange, H (Erlangen)
Thursday 21 April 2011, 14:0015:00
Fri, 06 May 2011 10:52:11 +0100
Lange, H
Steve Greenham
Isaac Newton Institute
Lange, H
6b1fcde3db82159ddaf0cf36593de313
fb8de191b215d695a1d70b9eb30c8909
a0764cfd35be30ee453acc930dbd1901
Lange, H (Erlangen)
Thursday 21 April 2011, 14:0015:00
Lange, H (Erlangen)
Thursday 21 April 2011, 14:0015:00
Cambridge University
3942
http://sms.cam.ac.uk/media/1137296
Generalisation of the tetragonal construction
Lange, H (Erlangen)
Thursday 21 April 2011, 14:0015:00
The Donagi conjecture states that the Prym map is injective at a double cover of a curve if the curve does not admit a morphism of degree less or equal to 4 onto the projective line. The talk focusses on 2 subjects, I will explain why the existing proofs of the tetragonal construction do not generalize and then outline the proof of a generalization which give counterexamples to the conjecture. This is joint work with Elham Izadi.
20110506T10:52:19+01:00
3942
1137296
true
16x9
false
no

Geometric Invariant Theory  I
ucs_sms_1087487_1087630
http://sms.cam.ac.uk/media/1087630
Geometric Invariant Theory  I
Doran, B (ETH Zürich)
Wednesday 05 January 2011, 14:0015:00
Thu, 06 Jan 2011 09:49:43 +0000
Doran, B
Steve Greenham
Isaac Newton Institute
Doran, B
a7c614f7c259d36bea877b05db32f112
94b3dd9d9b383c9877f58432266ad5a6
e3b22615aeadc407768436c8fd24608e
Doran, B (ETH Zürich)
Wednesday 05 January 2011, 14:0015:00
Doran, B (ETH Zürich)
Wednesday 05 January 2011, 14:0015:00
Cambridge University
3841
http://sms.cam.ac.uk/media/1087630
Geometric Invariant Theory  I
Doran, B (ETH Zürich)
Wednesday 05 January 2011, 14:0015:00
20110106T09:49:48+00:00
3841
1087630
true
16x9
false
no

Geometric Invariant Theory  II
ucs_sms_1087487_1087997
http://sms.cam.ac.uk/media/1087997
Geometric Invariant Theory  II
Doran, B (ETH Zürich)
Thursday 06 January 2011, 14:0015:00
Thu, 06 Jan 2011 17:42:47 +0000
Doran, B
Steve Greenham
Isaac Newton Institute
Doran, B
ad50000733a5788206abd9f9410c51a8
09e3d6ccb33004365c04c70d2e49f7df
7a1b26373801cafa733f27e0edc1bd0d
Doran, B (ETH Zürich)
Thursday 06 January 2011, 14:0015:00
Doran, B (ETH Zürich)
Thursday 06 January 2011, 14:0015:00
Cambridge University
4023
http://sms.cam.ac.uk/media/1087997
Geometric Invariant Theory  II
Doran, B (ETH Zürich)
Thursday 06 January 2011, 14:0015:00
20110106T17:42:51+00:00
4023
1087997
true
16x9
false
no

Geometric Invariant Theory  III
ucs_sms_1087487_1088858
http://sms.cam.ac.uk/media/1088858
Geometric Invariant Theory  III
Doran, B (ETH Zürich)
Friday 07 January 2011, 14:0015:00
Mon, 10 Jan 2011 13:01:22 +0000
Doran, B
Steve Greenham
Isaac Newton Institute
Doran, B
2e0d82723562bb4873b57079f9dfbbd2
dc131eb30a6709e5c5cb63663432351e
57bc039f974008f7f6372327497dcc2c
Doran, B (ETH Zürich)
Friday 07 January 2011, 14:0015:00
Doran, B (ETH Zürich)
Friday 07 January 2011, 14:0015:00
Cambridge University
3829
http://sms.cam.ac.uk/media/1088858
Geometric Invariant Theory  III
Doran, B (ETH Zürich)
Friday 07 January 2011, 14:0015:00
20110111T17:33:17+00:00
3829
1088858
true
16x9
false
no

Geometric Invariant Theory  IV
ucs_sms_1087487_1090943
http://sms.cam.ac.uk/media/1090943
Geometric Invariant Theory  IV
Doran, B (ETH Zürich)
Monday 10 January 2011, 10:0011:00
Thu, 13 Jan 2011 09:16:01 +0000
Doran, B
Tim Cooper
Isaac Newton Institute
Doran, B
7d09d9124273baadc554fe23c031051a
2e0a974377c62d967d28fe4917c8801a
8342386e55065919e73b7f83d3f4a0f5
b6c5c8b2be962a798317f1e3ed8fbb23
Doran, B (ETH Zürich)
Monday 10 January 2011, 10:0011:00
Doran, B (ETH Zürich)
Monday 10 January 2011, 10:0011:00
Cambridge University
3974
http://sms.cam.ac.uk/media/1090943
Geometric Invariant Theory  IV
Doran, B (ETH Zürich)
Monday 10 January 2011, 10:0011:00
20111222T09:09:54+00:00
3974
1090943
true
4x3
false
no

Geometric unitarity of the KZ/Hitchin connection on conformal blocks in genus 0
ucs_sms_1087487_1154436
http://sms.cam.ac.uk/media/1154436
Geometric unitarity of the KZ/Hitchin connection on conformal blocks in genus 0
Belkale, P (North Carolina)
Tuesday 28 June 2011, 10:0011:00
Wed, 29 Jun 2011 16:49:41 +0100
Belkale, P
Steve Greenham
Isaac Newton Institute
Belkale, P
dd276020cc6d6554cbb06fdc679b309b
3d1f79aeac6a1fbbec26e263db9fbc9e
c6545eeecc34b5f6df87f7235c47023e
Belkale, P (North Carolina)
Tuesday 28 June 2011, 10:0011:00
Belkale, P (North Carolina)
Tuesday 28 June 2011, 10:0011:00
Cambridge University
3598
http://sms.cam.ac.uk/media/1154436
Geometric unitarity of the KZ/Hitchin connection on conformal blocks in genus 0
Belkale, P (North Carolina)
Tuesday 28 June 2011, 10:0011:00
We prove that the vector bundles of conformal blocks, on moduli spaces of genus zero curves with marked points, for arbitrary simple Lie algebras and arbitrary integral levels, carry geometrically defined unitary metrics (as conjectured by K. Gawedzki) which are preserved by the KnizhnikZamolodchikov/Hitchin connection. Our proof builds upon the work of T. R. Ramadas who proved this unitarity statement in the case of the Lie algebra sl(2) (and genus zero) and arbitrary integral level.
20110629T16:49:50+01:00
3598
1154436
true
16x9
false
no

Higgs bundles and Hermitian symmetric spaces
ucs_sms_1087487_1154377
http://sms.cam.ac.uk/media/1154377
Higgs bundles and Hermitian symmetric spaces
Rubio, R (Oxford)
Monday 27 June 2011, 14:4015:10
Wed, 29 Jun 2011 16:18:20 +0100
Rubio, R
Steve Greenham
Isaac Newton Institute
Rubio, R
8a650fba636c8bd82cbf670da9e131ca
b53b9315e01cfad33e6715519115f992
1cb39bece93f964ab7ce83a28e3475b5
Rubio, R (Oxford)
Monday 27 June 2011, 14:4015:10
Rubio, R (Oxford)
Monday 27 June 2011, 14:4015:10
Cambridge University
1610
http://sms.cam.ac.uk/media/1154377
Higgs bundles and Hermitian symmetric spaces
Rubio, R (Oxford)
Monday 27 June 2011, 14:4015:10
We study the moduli space of polystable GHiggs bundles for noncompact real Lie groups G of Hermitian type. First, we define the Toledo character and use it to define the Toledo invariant, for which a MilnorWood type inequality is proved. Then, for the maximal value of the Toledo invariant, we state a Cayley correspondence for groups of socalled tube type and point out a rigidity theorem for groups of socalled nontube type. The proofs of these results are based on the Jordan algebra structure related to the tangent space of the Hermitian symmetric space given by G and are independent of the classification theorem of Lie groups. (Joint work with O. Biquard and Ó. GarcíaPrada.)
20110629T16:18:29+01:00
1610
1154377
true
16x9
false
no

Higgs bundles and quaternionic geometry
ucs_sms_1087487_1155115
http://sms.cam.ac.uk/media/1155115
Higgs bundles and quaternionic geometry
Hitchin, NJ (Oxford)
Friday 01 July 2011, 11:3012:30
Mon, 04 Jul 2011 10:01:16 +0100
Hitchin, NJ
Steve Greenham
Isaac Newton Institute
Hitchin, NJ
b9e9d52d8687734cfa7c2f8d157ba138
157fcab3749140ba3733ebc66e1e6947
ccdfdc12894d5e4b71337ec3f817eb20
Hitchin, NJ (Oxford)
Friday 01 July 2011, 11:3012:30
Hitchin, NJ (Oxford)
Friday 01 July 2011, 11:3012:30
Cambridge University
3932
http://sms.cam.ac.uk/media/1155115
Higgs bundles and quaternionic geometry
Hitchin, NJ (Oxford)
Friday 01 July 2011, 11:3012:30
The circle action on the moduli space of Higgs bundles provides a link between hyperkahler geometry and quaternionic Kahler geometry. The lecture will discuss various aspects of this.
20110704T10:01:25+01:00
3932
1155115
true
16x9
false
no

Higgs bundles for the noncompact dual of the unitary group
ucs_sms_1087487_1105274
http://sms.cam.ac.uk/media/1105274
Higgs bundles for the noncompact dual of the unitary group
Oliveira, A (TrásosMontes and Alto Douro)
Tuesday 01 March 2011, 11:3012:30
Fri, 04 Mar 2011 10:49:56 +0000
Oliveira, A
Steve Greenham
Isaac Newton Institute
Oliveira, A
c84cef8d26524962af20c5c1d5efdc11
f448a8237c5ae74626d0c8741f98240e
fc94ca6d157ccc645f969a41295086f5
Oliveira, A (TrásosMontes and Alto Douro)
Tuesday 01 March 2011, 11:3012:30
Oliveira, A (TrásosMontes and Alto Douro)
Tuesday 01 March 2011, 11:3012:30
Cambridge University
3540
http://sms.cam.ac.uk/media/1105274
Higgs bundles for the noncompact dual of the unitary group
Oliveira, A (TrásosMontes and Alto Douro)
Tuesday 01 March 2011, 11:3012:30
We show that the moduli space of U*(2n)Higgs bundles over a compact Riemann surface is connected. We adopt the Morsetheoretic approach pioneered by Hitchin, and which has already been applied for several other groups, to reduce our problem to the study of connectedness of certain subvarieties of the moduli space. Joint work with O. GarcíaPrada.
20110304T10:50:02+00:00
3540
1105274
true
16x9
false
no

Hilbert schemes of singular plane curves and HOMFLY homology of their links
ucs_sms_1087487_1132254
http://sms.cam.ac.uk/media/1132254
Hilbert schemes of singular plane curves and HOMFLY homology of their links
Shende, V (Princeton)
Thursday 14 April 2011, 15:0016:00
Mon, 18 Apr 2011 11:39:24 +0100
Shende, V
Steve Greenham
Isaac Newton Institute
Shende, V
d46909e5e1de79d191eb84d8251a0ab6
0ed9c38ec934911286714df487a9c245
f5cb2bc62ae647782c1846c3b6012630
Shende, V (Princeton)
Thursday 14 April 2011, 15:0016:00
Shende, V (Princeton)
Thursday 14 April 2011, 15:0016:00
Cambridge University
3469
http://sms.cam.ac.uk/media/1132254
Hilbert schemes of singular plane curves and HOMFLY homology of their links
Shende, V (Princeton)
Thursday 14 April 2011, 15:0016:00
Intersecting a plane curve with the boundary of a small ball around one of its singularities yields a link in the 3sphere. To any link may be attached a triply graded vector space, the HOMFLY homology. Taking its Euler characteristic with respect to a certain grading gives the HOMFLY polynomial, which in turn specializes variously to the Alexander polynomial, the Jones polynomial, and the other SU(n) knot polynomials.
We will present a conjecture recovering this invariant from moduli spaces attached to the singular curve. Specifically, we form the Hilbert schemes of points of the curve, and certain incidence varieties inside products of Hilbert schemes. Up to certain shifts of grading, we conjecture that the HOMFLY homology of the link of the singularity is the direct sum of the homologies of these spaces.
This talk presents joint work with J. Rasmussen and A. Oblomkov.
20110418T11:39:32+01:00
3469
1132254
true
16x9
false
no

Hodge polynomials of the moduli space of SL (2,C)  character varieties
ucs_sms_1087487_1095999
http://sms.cam.ac.uk/media/1095999
Hodge polynomials of the moduli space of SL (2,C)  character varieties
Logares, M (ICMAT)
Thursday 03 February 2011, 15:3016:30
Tue, 08 Feb 2011 14:21:31 +0000
Logares, M
Steve Greenham
Isaac Newton Institute
Logares, M
b47c4cb1fe43eea995e89267626651dd
bdfb3792e39a81ea8d83743e19a6ef73
a02193a5582802ee1dd83365509d3b8a
Logares, M (ICMAT)
Thursday 03 February 2011, 15:3016:30
Logares, M (ICMAT)
Thursday 03 February 2011, 15:3016:30
Cambridge University
3818
http://sms.cam.ac.uk/media/1095999
Hodge polynomials of the moduli space of SL (2,C)  character varieties
Logares, M (ICMAT)
Thursday 03 February 2011, 15:3016:30
Let X be a compact Riemann surface of genus g. SL(2,C)character varieties of X are rich objects which lie in the intersection of algebraic geometry, complex geometry, and differential geometry. While they are diffeomorphic to moduli spaces of Higgs bundles, as algebraic varieties they are very different. Character varieties are affine, while Higgs moduli spaces are foliated by the fibers of the Hitchin map which are compact algebraic subvarieties. There has been much work investigating the mixed Hodge structures on the cohomology groups of these character varieties, and their Hodge polynomials have been computed using number theoretical techniques. Our goal is to compute the Hodge polynomial of SL(2,C)character varieties, by stratifying these spaces in such a way that Hodge structure theory gives simpler formulas for the strata, so we are allowed to compute the whole polynomials in terms of the Hodge polynomials of the strata. This is work in progress with V. Muñoz and P. Newstead.
20110208T14:21:37+00:00
3818
1095999
true
16x9
false
no

Hyperkahler implosion
ucs_sms_1087487_1154302
http://sms.cam.ac.uk/media/1154302
Hyperkahler implosion
Kirwan, F (Oxford)
Monday 27 June 2011, 11:3012:30
Wed, 29 Jun 2011 16:01:42 +0100
Kirwan, F
Steve Greenham
Isaac Newton Institute
Kirwan, F
c4ae33e01a32f028ba0cb85748cc9f31
cc15529d546ce660a2ec557e09666d87
7c0da2db5b6a1d41d65bbde1655ffea5
Kirwan, F (Oxford)
Monday 27 June 2011, 11:3012:30
Kirwan, F (Oxford)
Monday 27 June 2011, 11:3012:30
Cambridge University
4106
http://sms.cam.ac.uk/media/1154302
Hyperkahler implosion
Kirwan, F (Oxford)
Monday 27 June 2011, 11:3012:30
Symplectic implosion is a construction in symplectic geometry due to Guillemin, Jeffrey and Sjamaar, which is related to geometric invariant theory for nonreductive group actions in algebraic geometry. This talk (based on joint work in progress with Andrew Dancer and Andrew Swann) is concerned with an analogous construction in hyperkahler geometry.
20110629T16:01:50+01:00
4106
1154302
true
16x9
false
no

Hyperpolygons and moduli spaces of parabolic Higgs bundles
ucs_sms_1087487_1154331
http://sms.cam.ac.uk/media/1154331
Hyperpolygons and moduli spaces of parabolic Higgs bundles
Mandini, A (Técnica de Lisboa)
Monday 27 June 2011, 14:0014:30
Wed, 29 Jun 2011 16:10:27 +0100
Mandini, A
Steve Greenham
Isaac Newton Institute
Mandini, A
366876502e7a16bd174b214a44a0c88a
f5d7243d756382737728da3b612d96c6
a52973362976b9752fb27115f0227d4c
Mandini, A (Técnica de Lisboa)
Monday 27 June 2011, 14:0014:30
Mandini, A (Técnica de Lisboa)
Monday 27 June 2011, 14:0014:30
Cambridge University
2054
http://sms.cam.ac.uk/media/1154331
Hyperpolygons and moduli spaces of parabolic Higgs bundles
Mandini, A (Técnica de Lisboa)
Monday 27 June 2011, 14:0014:30
Given an ntuple of positive real numbers α we consider the hyperpolygon space X(α), the hyperkähler quotient analogue to the Kähler moduli space of polygons in R3. There exists an isomorphism between hyperpolygon spaces and moduli spaces of stable, rank2, holomorphically trivial parabolic Higgs bundles over CP1 with fixed determinant and tracefree Higgs field. This allows us to prove that hyperpolygon spaces X(α) undergo an elementary transformation in the sense of Mukai as α crosses a wall in the space of its admissible values. We describe the resulting changes in the core of X(α) as well as the changes in the nilpotent cone of the corresponding moduli spaces of PHBs. If time permits, we will explain how to obtain explicit formulas for the computation of the intersection numbers of the core components of X(α) and of the nilpotent cone components of the corresponding moduli spaces of PHBs. As a final application, we describe the cohomology ring structure of these moduli spaces of PHBs and of the components of their nilpotent cone. This is joint work with Leonor Godinho.
20110629T16:10:36+01:00
2054
1154331
true
16x9
false
no

Integrable systems, Mirror Symmetry and DonaldsonThomas invariants
ucs_sms_1087487_1132280
http://sms.cam.ac.uk/media/1132280
Integrable systems, Mirror Symmetry and DonaldsonThomas invariants
Soibelman, I (Kansas State)
Friday 15 April 2011, 09:3010:30
Mon, 18 Apr 2011 11:53:54 +0100
Soibelman, I
Steve Greenham
Isaac Newton Institute
Soibelman, I
a33306c6eb94f9cf7a8c7fa872b43c68
f0fe81ad3ac86430b9a5bcd4cf690f58
3d925015aff9d417f0cee6c1fe7ce8b4
Soibelman, I (Kansas State)
Friday 15 April 2011, 09:3010:30
Soibelman, I (Kansas State)
Friday 15 April 2011, 09:3010:30
Cambridge University
3923
http://sms.cam.ac.uk/media/1132280
Integrable systems, Mirror Symmetry and DonaldsonThomas invariants
Soibelman, I (Kansas State)
Friday 15 April 2011, 09:3010:30
This talk is about applications of some ideas from Mirror Symmetry to complex integrable systems. It is a joint work with Maxim Kontsevich, and it is related to our theory of DonaldsonThomas invariants for 3d CalabiYau categories. In particular, wallcrossing formulas lead to a construction of ``exponential Hodge structure of infinite type".
20110418T11:54:02+01:00
3923
1132280
true
16x9
false
no

Introduction to a motivic point of view on the cohomology of moduli spaces of bundles on curves
ucs_sms_1087487_1113925
http://sms.cam.ac.uk/media/1113925
Introduction to a motivic point of view on the cohomology of moduli spaces of bundles on curves
Heinloth, J (Amsterdam)
Thursday 10 March 2011, 14:0015:00
Fri, 18 Mar 2011 09:18:31 +0000
Heinloth, J
Steve Greenham
Isaac Newton Institute
Heinloth, J
a24e911bec21018b6a214749a809557d
2dd48040e6152c9dc19c263406b96126
71294598e0d04dfe1e6971de3aead689
Heinloth, J (Amsterdam)
Thursday 10 March 2011, 14:0015:00
Heinloth, J (Amsterdam)
Thursday 10 March 2011, 14:0015:00
Cambridge University
4173
http://sms.cam.ac.uk/media/1113925
Introduction to a motivic point of view on the cohomology of moduli spaces of bundles on curves
Heinloth, J (Amsterdam)
Thursday 10 March 2011, 14:0015:00
For moduli spaces of vector bundles on curves and some moduli spaces of Higgs bundles, it is possible to compute their cohomology groups in a geometric way, i.e., one can describe the space by a cutandpaste procedure in terms of cells and symmetric products of the base curve. This gives a rather explicit description of the "motive" of the space. For moduli space of vector bundles this is due to Behrend and Dhillon, relying on an argument of Bifet, Ghione, and Letizia. We will try to give an introduction to this point of view on cohomology calcuations for moduli spaces.
20110318T09:18:38+00:00
4173
1113925
true
16x9
false
no

Introduction to derived categories and stability conditions  I
ucs_sms_1087487_1090983
http://sms.cam.ac.uk/media/1090983
Introduction to derived categories and stability conditions  I
Huybrechts, D (Bonn)
Monday 10 January 2011, 14:0015:00
Thu, 13 Jan 2011 09:49:22 +0000
Huybrechts, D
Tim Cooper
Isaac Newton Institute
Huybrechts, D
61532e38ddec92c88ed52d332fe26b55
1eb353ba4697df8b55773911e30bed4b
6bb5e25c0b0738d3b0f9e25d9ddd2673
01dcd26c942f348f10baf649fd0f39e8
d1e8908fb3fb5ab0f7de42c5bf00c471
Huybrechts, D (Bonn)
Monday 10 January 2011, 14:0015:00
Huybrechts, D (Bonn)
Monday 10 January 2011, 14:0015:00
Cambridge University
3792
http://sms.cam.ac.uk/media/1090983
Introduction to derived categories and stability conditions  I
Huybrechts, D (Bonn)
Monday 10 January 2011, 14:0015:00
The title may be misleading, I will actually assume the audience to be familiar with the basic concepts of derived and triangulated categories. (I might however recall the notion of tstructures.) The emphasis will be on stability conditions. I plan to introduce stability conditions in the sense of Bridgeland (and KontsevichSoibelman) and discuss examples. The relevant literature is accessible on the arxiv.
20110113T09:49:27+00:00
3792
1090983
true
4x3
false
no

Introduction to derived categories and stability conditions  II
ucs_sms_1087487_1091162
http://sms.cam.ac.uk/media/1091162
Introduction to derived categories and stability conditions  II
Huybrechts, D (Bonn)
Tuesday 11 January 2011, 14:0015:00
Thu, 13 Jan 2011 18:08:29 +0000
Huybrechts, D
Tim Cooper
Isaac Newton Institute
Huybrechts, D
1b1826ea41e068e466a49187f203b82b
d170eaf0c845893e165f5216ab0a9c1f
832705ed3b0cd770a26471e3978a2de2
6cb7a45a6fe108f174370e657465ffff
482adcfa04075a2c848d75394ece044c
Huybrechts, D (Bonn)
Tuesday 11 January 2011, 14:0015:00
Huybrechts, D (Bonn)
Tuesday 11 January 2011, 14:0015:00
Cambridge University
3739
http://sms.cam.ac.uk/media/1091162
Introduction to derived categories and stability conditions  II
Huybrechts, D (Bonn)
Tuesday 11 January 2011, 14:0015:00
The title may be misleading, I will actually assume the audience to be familiar with the basic concepts of derived and triangulated categories. (I might however recall the notion of tstructures.) The emphasis will be on stability conditions. I plan to introduce stability conditions in the sense of Bridgeland (and KontsevichSoibelman) and discuss examples. The relevant literature is accessible on the arxiv.
20110113T18:08:33+00:00
3739
1091162
true
4x3
false
no

Introduction to derived categories and stability conditions  III
ucs_sms_1087487_1091289
http://sms.cam.ac.uk/media/1091289
Introduction to derived categories and stability conditions  III
Huybrechts, D (Bonn)
Wednesday 12 January 2011, 14:0015:00
Wed, 19 Jan 2011 12:31:52 +0000
Huybrechts, D
Tim Cooper
Isaac Newton Institute
Huybrechts, D
2405ca9df473749fe5e03fcc2c6e7400
890dc010baba61589506361a5c3cf6fc
f4a76ac19b72591ab23570c2a7c52326
50353a6dbcbdc8f010c632d72316d766
9280d811da7e89fcaf7c11d1aac3c275
Huybrechts, D (Bonn)
Wednesday 12 January 2011, 14:0015:00
Huybrechts, D (Bonn)
Wednesday 12 January 2011, 14:0015:00
Cambridge University
3796
http://sms.cam.ac.uk/media/1091289
Introduction to derived categories and stability conditions  III
Huybrechts, D (Bonn)
Wednesday 12 January 2011, 14:0015:00
The title may be misleading, I will actually assume the audience to be familiar with the basic concepts of derived and triangulated categories. (I might however recall the notion of tstructures.) The emphasis will be on stability conditions. I plan to introduce stability conditions in the sense of Bridgeland (and KontsevichSoibelman) and discuss examples. The relevant literature is accessible on the arxiv.
20110119T12:32:03+00:00
3796
1091289
true
4x3
false
no

Introduction to derived categories and stability conditions  V
ucs_sms_1087487_1091445
http://sms.cam.ac.uk/media/1091445
Introduction to derived categories and stability conditions  V
Huybrechts, D (Bonn)
Friday 14 January 2011, 14:0015:00
Fri, 14 Jan 2011 19:47:31 +0000
Huybrechts, D
Tim Cooper
Isaac Newton Institute
Huybrechts, D
bb5e23b55f1f557f8f20a98259837fc7
20e0111a8f70458682e46e0726170f1b
eeebf9eb0255cae68a0425fde7d708e3
ca80f5999e96c72fde08de26ee8004da
8b956272b5c08c3b4d8d137f07c19104
Huybrechts, D (Bonn)
Friday 14 January 2011, 14:0015:00
Huybrechts, D (Bonn)
Friday 14 January 2011, 14:0015:00
Cambridge University
3613
http://sms.cam.ac.uk/media/1091445
Introduction to derived categories and stability conditions  V
Huybrechts, D (Bonn)
Friday 14 January 2011, 14:0015:00
The title may be misleading, I will actually assume the audience to be familiar with the basic concepts of derived and triangulated categories. (I might however recall the notion of tstructures.) The emphasis will be on stability conditions. I plan to introduce stability conditions in the sense of Bridgeland (and KontsevichSoibelman) and discuss examples. The relevant literature is accessible on the arxiv.
20110114T19:47:37+00:00
3613
1091445
true
4x3
false
no

Introduction to moduli of varieties  I: Generalities on moduli spaces of varieties
ucs_sms_1087487_1090916
http://sms.cam.ac.uk/media/1090916
Introduction to moduli of varieties  I: Generalities on moduli spaces of varieties
Alexeev, V (Georgia)
Monday 10 January 2011, 15:3016:30
Thu, 13 Jan 2011 08:59:11 +0000
Alexeev, V
Tim Cooper
Isaac Newton Institute
Alexeev, V
edd5fb2f3b792ddf02a3c2c4f8a648d0
9b41e9f54509dd172f95a64ae55bb6ee
ed9c5f1f239ce8c0f8883b9a489068be
dac9a7ac0d5b2e11f7dcd8a0f8a1aaa1
ebc37776867eb3008f3ba59f1d14b859
Alexeev, V (Georgia)
Monday 10 January 2011, 15:3016:30
Alexeev, V (Georgia)
Monday 10 January 2011, 15:3016:30
Cambridge University
4054
http://sms.cam.ac.uk/media/1090916
Introduction to moduli of varieties  I: Generalities on moduli spaces of varieties
Alexeev, V (Georgia)
Monday 10 January 2011, 15:3016:30
The yoga of moduli spaces. Main methods of construction. Compactifications and Minimal Model Program. Stable pairs (slc & ample K+B). Honest work vs "accidental" examples.
20110113T08:59:16+00:00
4054
1090916
true
4x3
false
no

Introduction to moduli of varieties  II: Stable toric and semiabelic varieties
ucs_sms_1087487_1091190
http://sms.cam.ac.uk/media/1091190
Introduction to moduli of varieties  II: Stable toric and semiabelic varieties
Alexeev, V (Georgia)
Tuesday 11 January 2011, 15:3016:30
Thu, 13 Jan 2011 18:34:01 +0000
Alexeev, V
Tim Cooper
Isaac Newton Institute
Alexeev, V
8cc7805606e7483191ec2a0c53bf2ab1
73b97f89566bb86a2244a85010509836
38f7e6596a5cf4c16b7d8a0da8a44da0
45b88e2fe924055d3d4c4613361492d5
823ad2d9fe13ed8a1066f63fa10c0dd0
Alexeev, V (Georgia)
Tuesday 11 January 2011, 15:3016:30
Alexeev, V (Georgia)
Tuesday 11 January 2011, 15:3016:30
Cambridge University
3999
http://sms.cam.ac.uk/media/1091190
Introduction to moduli of varieties  II: Stable toric and semiabelic varieties
Alexeev, V (Georgia)
Tuesday 11 January 2011, 15:3016:30
Moduli of stable toric varieties vs toric Hilbert scheme. Convex tilings and secondary polytopes. Degenerations of abelian varieties. Semiabelian and semiabelic varieties. Compactifications of moduli spaces of abelian varieties.
Refs: http://arxiv.org/abs/math/9905103, http://arxiv.org/abs/math/0207272, http://arxiv.org/abs/math/0207274.
20110113T18:34:06+00:00
3999
1091190
true
4x3
false
no

Introduction to moduli of varieties  III: Weighted hyperplane arrangements
ucs_sms_1087487_1091317
http://sms.cam.ac.uk/media/1091317
Introduction to moduli of varieties  III: Weighted hyperplane arrangements
Alexeev, V (Georgia)
Wednesday 12 January 2011, 15:3016:30
Wed, 19 Jan 2011 12:50:55 +0000
Alexeev, V
Tim Cooper
Isaac Newton Institute
Alexeev, V
acea5cc1c3f0c1eba61cb0c1e4b3a1d5
7161790f1a026257742ef77fbd9c648a
d1062d70ca438fb8effb283a77af9c97
451fc0684ce32820a493ea84d262a76f
50846f656d73098eb2eb3bb266560389
Alexeev, V (Georgia)
Wednesday 12 January 2011, 15:3016:30
Alexeev, V (Georgia)
Wednesday 12 January 2011, 15:3016:30
Cambridge University
4035
http://sms.cam.ac.uk/media/1091317
Introduction to moduli of varieties  III: Weighted hyperplane arrangements
Alexeev, V (Georgia)
Wednesday 12 January 2011, 15:3016:30
Mˉ0,n. Hassett's weighted stable curves. Compact moduli of weighted hyperplane arrangements.
Refs: http://arxiv.org/abs/math/0205009, http://arxiv.org/abs/math/0501227, http://arxiv.org/abs/0806.0881
20110119T12:51:04+00:00
4035
1091317
true
4x3
false
no

Introduction to moduli of varieties  IV: Surfaces of general type related to abelian varieties and hyperplane arrangements
ucs_sms_1087487_1154803
http://sms.cam.ac.uk/media/1154803
Introduction to moduli of varieties  IV: Surfaces of general type related to abelian varieties and hyperplane arrangements
Alexeev, V (Georgia)
Thursday 13 January 2011, 15:3016:30
Fri, 01 Jul 2011 14:42:45 +0100
Alexeev, V
Tim Cooper
Irene Galstian
Isaac Newton Institute
Alexeev, V
a8f1fe251f3512a33c024c0e5ca7b809
da7d95841918f1b487aa2a1b7a4cf965
724d8d2be75f140d72ef3d45ade44bed
Alexeev, V (Georgia)
Thursday 13 January 2011, 15:3016:30
Alexeev, V (Georgia)
Thursday 13 January 2011, 15:3016:30
Cambridge University
3924
http://sms.cam.ac.uk/media/1154803
Introduction to moduli of varieties  IV: Surfaces of general type related to abelian varieties and hyperplane arrangements
Alexeev, V (Georgia)
Thursday 13 January 2011, 15:3016:30
Compact moduli of surfaces of general type derived from (1) abelian varieties, (2) line arrangements. Campedelli, Burniat, Kulikov surfaces.
Refs: http://arxiv.org/abs/math/9905103, http://arxiv.org/abs/0901.4431
20110701T15:01:04+01:00
3924
1154803
true
16x9
false
no

Introduction to moduli of varieties  V: Surfaces of general type: the general case
ucs_sms_1087487_1091499
http://sms.cam.ac.uk/media/1091499
Introduction to moduli of varieties  V: Surfaces of general type: the general case
Alexeev, V (Georgia)
Friday 14 January 2011, 15:3016:30
Mon, 17 Jan 2011 09:06:13 +0000
Alexeev, V
Tim Cooper
Isaac Newton Institute
Alexeev, V
7e02309ee7d58439cdd034c7e470eeb3
574dfd9bb9bafdf30f8551bd9b72ef5b
185fc8c67fcaecb0977a490a765a1866
ce7cc956b2861c36afffaf327074a4a5
35c3afb6b7f406e5f4e6b097efed597e
Alexeev, V (Georgia)
Friday 14 January 2011, 15:3016:30
Alexeev, V (Georgia)
Friday 14 January 2011, 15:3016:30
Cambridge University
4085
http://sms.cam.ac.uk/media/1091499
Introduction to moduli of varieties  V: Surfaces of general type: the general case
Alexeev, V (Georgia)
Friday 14 January 2011, 15:3016:30
Several versions of the moduli functor. Problems, and some solutions. Steps in the construction of the moduli space.
Ref: many older papers, http://arxiv.org/abs/0805.0576, http://arxiv.org/abs/1008.0621 (by Kollár)
20110117T09:06:18+00:00
4085
1091499
true
4x3
false
no

Introduction to stacks  I
ucs_sms_1087487_1091092
http://sms.cam.ac.uk/media/1091092
Introduction to stacks  I
Behrend, K (British Columbia)
Tuesday 11 January 2011, 10:0011:00
Thu, 13 Jan 2011 15:06:12 +0000
Behrend, K
Tim Cooper
Isaac Newton Institute
Behrend, K
78f35fee2814042665b0aeeb8e0ff6fa
738abde20a3d9a1b3a9773d9118308ee
ce722fd5786928e4229046a797d56c2a
23d565423a73936fe77992970cc1cb8a
289e81cab68e5e640bdb023af22f8555
Behrend, K (British Columbia)
Tuesday 11 January 2011, 10:0011:00
Behrend, K (British Columbia)
Tuesday 11 January 2011, 10:0011:00
Cambridge University
3871
http://sms.cam.ac.uk/media/1091092
Introduction to stacks  I
Behrend, K (British Columbia)
Tuesday 11 January 2011, 10:0011:00
Introduction to algebraic stacks as they are relevant to moduli theory.
20110113T15:06:17+00:00
3871
1091092
true
4x3
false
no

Introduction to stacks  II
ucs_sms_1087487_1091215
http://sms.cam.ac.uk/media/1091215
Introduction to stacks  II
Behrend, K (British Columbia)
Wednesday 12 January 2011, 10:0011:00
Thu, 13 Jan 2011 18:51:52 +0000
Behrend, K
Tim Cooper
Isaac Newton Institute
Behrend, K
287768c7393d1639af5c8d2e7fe79794
1803a374e6b75a3772faa1fa54956953
9ebfa8a41c514f46d1dfe1e18b942637
9f3ddd58141cca3918073572252015d7
1f4fd2fb5d3f2ffb5a3ef8af3adcbdc0
Behrend, K (British Columbia)
Wednesday 12 January 2011, 10:0011:00
Behrend, K (British Columbia)
Wednesday 12 January 2011, 10:0011:00
Cambridge University
4042
http://sms.cam.ac.uk/media/1091215
Introduction to stacks  II
Behrend, K (British Columbia)
Wednesday 12 January 2011, 10:0011:00
Introduction to algebraic stacks as they are relevant to moduli theory.
20110113T18:51:57+00:00
4042
1091215
true
4x3
false
no

Introduction to stacks  IV
ucs_sms_1087487_1091389
http://sms.cam.ac.uk/media/1091389
Introduction to stacks  IV
Behrend, K (British Columbia)
Friday 14 January 2011, 10:0011:00
Fri, 14 Jan 2011 19:08:01 +0000
Behrend, K
Tim Cooper
Isaac Newton Institute
Behrend, K
f131d03be2e9793c5bb0d8be59aba455
f6849426ff25b34f2860b1846ca89a29
841073a476c4b4d0c7448808a811f8c0
be7c6b092c77f328a4524cc4176c8916
76c710732c7c72c0e6aeeb271adb72a5
Behrend, K (British Columbia)
Friday 14 January 2011, 10:0011:00
Behrend, K (British Columbia)
Friday 14 January 2011, 10:0011:00
Cambridge University
4787
http://sms.cam.ac.uk/media/1091389
Introduction to stacks  IV
Behrend, K (British Columbia)
Friday 14 January 2011, 10:0011:00
Introduction to algebraic stacks as they are relevant to moduli theory.
20110114T19:08:06+00:00
4787
1091389
true
4x3
false
no

K3 surfaces of genus 17
ucs_sms_1087487_1131798
http://sms.cam.ac.uk/media/1131798
K3 surfaces of genus 17
Mukai, S (Kyoto)
Tuesday 12 April 2011, 15:0016:00
Fri, 15 Apr 2011 16:23:03 +0100
Mukai, S
Steve Greenham
Isaac Newton Institute
Mukai, S
dc71f7b829278ad7b7426378eadba863
c42935da1d13ff46ffae310b8c63314d
999fb208dbf811cc5efe1b43bb77d1c3
Mukai, S (Kyoto)
Tuesday 12 April 2011, 15:0016:00
Mukai, S (Kyoto)
Tuesday 12 April 2011, 15:0016:00
Cambridge University
3657
http://sms.cam.ac.uk/media/1131798
K3 surfaces of genus 17
Mukai, S (Kyoto)
Tuesday 12 April 2011, 15:0016:00
The moduli space M=M(2, h, 8) of semirigid vector bundles on a (polarized) K3 surface (S, h) of genus 17 is a K3 surface of genus 5. Moreover, the universal family gives an equivalence between the derived category of S and a twisted derived category of M. This equivalence induces us a rational map from S to the nonabelian BrillNoether locus SU(2, K; 5F) of type II (see alggeom/9704015) in the moduli space of 2bundles on a curve of genus 5. We show that this map is an isomorphism when the modulus of (S, h) is general, using Thaddeus' formula. As a corollary the moduli space F17 of (S, h)’s is unirational.
20110415T16:23:11+01:00
3657
1131798
true
16x9
false
no

KahlerEinstein metrics and Geometric Invariant Theory
ucs_sms_1087487_1154824
http://sms.cam.ac.uk/media/1154824
KahlerEinstein metrics and Geometric Invariant Theory
Donaldson, S (Imperial)
Thursday 30 June 2011, 10:0011:00
Fri, 01 Jul 2011 15:34:59 +0100
Donaldson, S
Steve Greenham
Isaac Newton Institute
Donaldson, S
3cdf6a0d950e67aa17b43bfb99ffb702
e0866be1a6403542a9976259847a7082
a4b4bfca57c6a5ad159aab37b103b07e
Donaldson, S (Imperial)
Thursday 30 June 2011, 10:0011:00
Donaldson, S (Imperial)
Thursday 30 June 2011, 10:0011:00
Cambridge University
3978
http://sms.cam.ac.uk/media/1154824
KahlerEinstein metrics and Geometric Invariant Theory
Donaldson, S (Imperial)
Thursday 30 June 2011, 10:0011:00
I will discuss an approach to a version of Yau's conjecture, relating KahlerEinstein metrics to notions of stability. The core of this approach involves estimates for the Chow invariant, obtained from asymptotic analysis. We will also describe progress on a variant of the setup involving an anticanonical divisor, somewhat analogous to the theory of parabolic bundles. Another theme in the talk will be the importance of making progress on testing stability in explicit cases.
20110701T15:35:08+01:00
3978
1154824
true
16x9
false
no

Kirwan blowups and moduli spaces
ucs_sms_1087487_1093951
http://sms.cam.ac.uk/media/1093951
Kirwan blowups and moduli spaces
Kiem, YH (Seoul National University)
Tuesday 25 January 2011, 11.3012.30
Thu, 27 Jan 2011 15:20:06 +0000
Kiem, YH
Steve Greenham
Isaac Newton Institute
Kiem, YH
8aff2ed9006968e6660b404a55f9de40
3308f29a2f009c61beddfcb014770a54
717747cc31a5684d6f234b23ae1c7aee
Kiem, YH (Seoul National University)
Tuesday 25 January 2011, 11.3012.30
Kiem, YH (Seoul National University)
Tuesday 25 January 2011, 11.3012.30
Cambridge University
3762
http://sms.cam.ac.uk/media/1093951
Kirwan blowups and moduli spaces
Kiem, YH (Seoul National University)
Tuesday 25 January 2011, 11.3012.30
Kirwan's partial desingularization is a sequence of blowups which systematically resolves the strictly semistable points in geometric invariant theory. In this talk, I will discuss various examples of moduli spaces constructed by Kirwan blowups such as the moduli space of stable maps of degree 2, the moduli space of Hecke curves and the moduli space of weighted pointed rational curves. If time permits, I will also talk about a joint project with Jun Li in which we study wall crossing and (generalized) DonaldsonThomas type invariants by using Kirwan blowups.
20110127T15:20:12+00:00
3762
1093951
true
16x9
false
no

Linear stability and stability of dual span bundles
ucs_sms_1087487_1149209
http://sms.cam.ac.uk/media/1149209
Linear stability and stability of dual span bundles
Mistretta, E (Padova)
Thursday 09 June 2011, 15:3016:30
Mon, 13 Jun 2011 11:59:51 +0100
Mistretta, E
Steve Greenham
Isaac Newton Institute
Mistretta, E
831bbe0aa15d74bc8168ddc95e7b3bd7
e44ce4fe00f0285cc6f6532d5efe47c5
7758c3784d75ab6535b79cd3c33b0533
Mistretta, E (Padova)
Thursday 09 June 2011, 15:3016:30
Mistretta, E (Padova)
Thursday 09 June 2011, 15:3016:30
Cambridge University
3797
http://sms.cam.ac.uk/media/1149209
Linear stability and stability of dual span bundles
Mistretta, E (Padova)
Thursday 09 June 2011, 15:3016:30
Dual span bundles have been constructed and used on many different purposes in algebraic geometry. The stability of these bundles has been proven in many cases and with different applications, from normal generation to the studying of the Picard sheaf, from the investigation on generalized thetadivisors, to that of coherent systems and BrillNoether loci. We discuss about a work in progress with Lidia Stoppino, relating the stability of these bundles to the linear stability of linear systems on curves as defined by Mumford, providing some questions, some examples, few answers, and illustrating some connection with Butler's conjecture on stability of dual span bundles.
20110613T12:00:00+01:00
3797
1149209
true
16x9
false
no

Localization in quiver moduli spaces and the Refined GW/Kronecker correspondence
ucs_sms_1087487_1149177
http://sms.cam.ac.uk/media/1149177
Localization in quiver moduli spaces and the Refined GW/Kronecker correspondence
Weist, T (Wuppertal)
Tuesday 07 June 2011, 11:3012:30
Mon, 13 Jun 2011 10:55:13 +0100
Weist, T
Steve Greenham
Isaac Newton Institute
Weist, T
da10640131cb79e1087904d1bda1651f
283a74ac2af55cd9384189068fc739c7
fb709b8a5aca2ecdedd0b635d6c39c89
Weist, T (Wuppertal)
Tuesday 07 June 2011, 11:3012:30
Weist, T (Wuppertal)
Tuesday 07 June 2011, 11:3012:30
Cambridge University
3891
http://sms.cam.ac.uk/media/1149177
Localization in quiver moduli spaces and the Refined GW/Kronecker correspondence
Weist, T (Wuppertal)
Tuesday 07 June 2011, 11:3012:30
GromovWitten invariants of weighted projective lines and Euler characteristics of moduli spaces of representations of bipartite quivers are related via the tropical vertex. Using localization techniques it is possible to give explicit formulas for the Euler characteristics in several cases which allows us to give explicit formulas of GromovWitten invariants.
20110613T10:55:22+01:00
3891
1149177
true
16x9
false
no

Logarithmic GromovWitten invariants
ucs_sms_1087487_1150259
http://sms.cam.ac.uk/media/1150259
Logarithmic GromovWitten invariants
Gross, M (UCSD)
Friday 17 June 2011, 14:0015:00
Tue, 21 Jun 2011 11:14:29 +0100
Gross, M
Steve Greenham
Isaac Newton Institute
Gross, M
b13af9ea3932917ee93a241a45f937d7
fdec22744485d5151ecc55cdd2c8a18f
d5f4733a3fae3546c3f55e7a0aefe5f0
Gross, M (UCSD)
Friday 17 June 2011, 14:0015:00
Gross, M (UCSD)
Friday 17 June 2011, 14:0015:00
Cambridge University
3774
http://sms.cam.ac.uk/media/1150259
Logarithmic GromovWitten invariants
Gross, M (UCSD)
Friday 17 June 2011, 14:0015:00
Relative GromovWitten invariants, which count curves with specified orders of tangency with a smooth divisor, have proven to be an extremely useful tool in GromovWitten theory: the gluing formula allows one to compute GW invariants of varieties by degenerating them to normal crossing unions of two varieties and then computing relative GW invariants on each of these varieties. Siebert and I propose a generalization of relative GW invariants which will allow tangency conditions with much more general divisors, and allow much more complicated degenerations.
20110621T11:14:38+01:00
3774
1150259
true
16x9
false
no

Minuscule varieties and their degenerations
ucs_sms_1087487_1131811
http://sms.cam.ac.uk/media/1131811
Minuscule varieties and their degenerations
Bondal, A (Steklov Institute in Moscow & IPMU (Japan) )
Tuesday 12 April 2011, 16:3017:30
Fri, 15 Apr 2011 16:32:49 +0100
Bondal, A
Steve Greenham
Isaac Newton Institute
Bondal, A
82f496c1b6992de5c227a59f5fc4770d
230c37aa78152dcc18e322b4cd8a1515
0054e38a0568ec976963e93ea5a40561
Bondal, A (Steklov Institute in Moscow & IPMU (Japan) )
Tuesday 12 April 2011,...
Bondal, A (Steklov Institute in Moscow & IPMU (Japan) )
Tuesday 12 April 2011, 16:3017:30
Cambridge University
3845
http://sms.cam.ac.uk/media/1131811
Minuscule varieties and their degenerations
Bondal, A (Steklov Institute in Moscow & IPMU (Japan) )
Tuesday 12 April 2011, 16:3017:30
We will give a description of toric degenerations of minuscule varieties in terms of moduli spaces of representations of quivers. We apply this to description of the structure of derived categories of coherent sheaves on minuscule varieties and to constructing LandauGinzburg models for them.
20110415T16:32:56+01:00
3845
1131811
true
16x9
false
no

Mirror symmetry for affine CalabiYaus
ucs_sms_1087487_1149140
http://sms.cam.ac.uk/media/1149140
Mirror symmetry for affine CalabiYaus
Keel, S (Texas)
Monday 06 June 2011, 15:3016:30
Mon, 13 Jun 2011 10:23:37 +0100
Keel, S
Steve Greenham
Isaac Newton Institute
Keel, S
92821ecda7083a727bd89c852f643ea8
ae530f36e853e98c89fb397bf0c13f73
47ec9cace7e7e3897a032e66e8b89375
Keel, S (Texas)
Monday 06 June 2011, 15:3016:30
Keel, S (Texas)
Monday 06 June 2011, 15:3016:30
Cambridge University
4280
http://sms.cam.ac.uk/media/1149140
Mirror symmetry for affine CalabiYaus
Keel, S (Texas)
Monday 06 June 2011, 15:3016:30
I will explain my recent conjecture joint with Hacking and Gross, and theorem in dimension two, which gives the mirror to an affine CY manifold of any dimensions as the Spec of an explicit algebra: The algebra comes with a basis parameterized by a Generalisation of Thurston's boundary sphere to Teichmuller space, and a multiplication rule in terms of counts of rational curves.
20110613T10:23:46+01:00
4280
1149140
true
16x9
false
no

Moduli in derived categories
ucs_sms_1087487_1137334
http://sms.cam.ac.uk/media/1137334
Moduli in derived categories
Lieblich, M (Washington)
Thursday 05 May 2011, 11:0012:00
Spitalfields Day
Fri, 06 May 2011 11:18:37 +0100
Lieblich, M
Steve Greenham
Isaac Newton Institute
Lieblich, M
230de4601cabf7c6efd4c63e00eaf128
edae06c78fcaa98a0ddd7ffbcd6ee8b7
0aaff05ccdf6172787531635acd05984
Lieblich, M (Washington)
Thursday 05 May 2011, 11:0012:00
Spitalfields Day
Lieblich, M (Washington)
Thursday 05 May 2011, 11:0012:00
Spitalfields Day
Cambridge University
3915
http://sms.cam.ac.uk/media/1137334
Moduli in derived categories
Lieblich, M (Washington)
Thursday 05 May 2011, 11:0012:00
Spitalfields Day
Classical moduli theory was born with a focus on objects we can easily see: varieties, vector bundles, morphisms, etc. In the last halfcentury, we have come to perceive a slew of subtler invariants, such as the derived category of coherent sheaves on a variety, that are decidedly murkier. Within the last decade, moduli spaces of objects in the derived category began to appear, drawing inspiration from birational geometry and mathematical physics. It turns out that a systematic approach to constructing these moduli spaces bears fruit in such disparate areas as GromovWitten theory, arithmetic geometry, and noncommutative algebra. I will describe some aspects of these moduli problems and a few of their principal applications.
20110506T11:18:45+01:00
3915
1137334
true
16x9
false
no

Moduli of local systems on DeligneMumford stacks
ucs_sms_1087487_1105458
http://sms.cam.ac.uk/media/1105458
Moduli of local systems on DeligneMumford stacks
Simpson, C (Nice)
Thursday 03 March 2011, 15:3016:30
Fri, 04 Mar 2011 11:53:57 +0000
Simpson, C
Steve Greenham
Isaac Newton Institute
Simpson, C
be9efe72a5f10b445224208d9f9f94e2
f29cfea72b8f56891d3f840ae66fddf4
f9467eb1ed2c916999e195cedd0a207c
Simpson, C (Nice)
Thursday 03 March 2011, 15:3016:30
Simpson, C (Nice)
Thursday 03 March 2011, 15:3016:30
Cambridge University
4317
http://sms.cam.ac.uk/media/1105458
Moduli of local systems on DeligneMumford stacks
Simpson, C (Nice)
Thursday 03 March 2011, 15:3016:30
Most aspects of the theory of moduli of local systems on smooth projective varieties extend to smooth (or even just normal) proper DMstacks, via a little covering lemma. For other singularities or simplicial varieties we meet a phenomenon of weight filtration. The DMstack case also allows us to approach the question of open varieties while avoiding the more difficult technical aspects there, and it provides a convenient formalism for finite group actions. In the example of a root stack over the projective line, the moduli space can have components containing no representations into a compact group.
20110304T11:54:03+00:00
4317
1105458
true
16x9
false
no

Moduli of plane sheaves supported on curves of low multiplicity
ucs_sms_1087487_1154487
http://sms.cam.ac.uk/media/1154487
Moduli of plane sheaves supported on curves of low multiplicity
Maican, M (IMRA)
Tuesday 28 June 2011, 14:0014:30
Wed, 29 Jun 2011 17:13:26 +0100
Maican, M
Steve Greenham
Isaac Newton Institute
Maican, M
645fafa934725001d6519454025a8622
8f26adfedc33b98c227c43d527717604
a894ddd8e76b9eebdb2da1c41d93000c
Maican, M (IMRA)
Tuesday 28 June 2011, 14:0014:30
Maican, M (IMRA)
Tuesday 28 June 2011, 14:0014:30
Cambridge University
1750
http://sms.cam.ac.uk/media/1154487
Moduli of plane sheaves supported on curves of low multiplicity
Maican, M (IMRA)
Tuesday 28 June 2011, 14:0014:30
We will classify the Gieseker semistable sheaves on the complex projective plane with support of dimension one and multiplicity four, five and, in some cases, multiplicity six. We will give natural stratifications for their moduli spaces. The strata are defined by means of cohomological conditions and have concrete geometric descriptions.
20110629T17:13:35+01:00
1750
1154487
true
16x9
false
no

Moduli of real and quaternionic bundles over a curve
ucs_sms_1087487_1113808
http://sms.cam.ac.uk/media/1113808
Moduli of real and quaternionic bundles over a curve
Schaffhauser, F (Los Andes, Bogota)
Tuesday 08 March 2011, 11:3012:30
Thu, 17 Mar 2011 17:36:09 +0000
Schaffhauser, F
Steve Greenham
Isaac Newton Institute
Schaffhauser, F
ea5923b5a191fa14957a6a5d68358edd
e02f4e5811764e402a8e775760225ffe
b3dfb88721b4605f18dae3d6ace8a623
Schaffhauser, F (Los Andes, Bogota)
Tuesday 08 March 2011, 11:3012:30
Schaffhauser, F (Los Andes, Bogota)
Tuesday 08 March 2011, 11:3012:30
Cambridge University
4247
http://sms.cam.ac.uk/media/1113808
Moduli of real and quaternionic bundles over a curve
Schaffhauser, F (Los Andes, Bogota)
Tuesday 08 March 2011, 11:3012:30
We examine a moduli problem for real and quaternionic vector bundles over a smooth complex projective curve, and we give a gaugetheoretic construction of moduli spaces for such bundles. These spaces are irreducible subsets of real points inside a complex projective variety. We relate our point of view to previous work by Biswas, Huisman and Hurtubise, and we use this to study the Gal(C/R)action on moduli varieties of semistable holomorphic bundles over a complex curve with given real structure \sigma. We show in particular a Harnacktype theorem, bounding the number of connected components of the fixedpoint set of this action by 2^g +1, where g is the genus of the curve. In fact, taking into account all the topological invariants of a real algebraic curve, we give an exact count of the number of connected components, thus generalizing to rank r \geq 2 the results of Gross and Harris on the Picard scheme of a real algebraic curve.
20110317T17:36:15+00:00
4247
1113808
true
16x9
false
no

Moduli of sheaves and strange duality
ucs_sms_1087487_1137360
http://sms.cam.ac.uk/media/1137360
Moduli of sheaves and strange duality
Marian, A (Illinois at Chicago)
Thursday 05 May 2011, 13:4514:45
Spitalfields Day
Fri, 06 May 2011 11:28:54 +0100
Marian, A
Steve Greenham
Isaac Newton Institute
Marian, A
41fef6e915fb17c7a2df2abaf56b042c
52561e4928cbb1d81285ee0d665fd663
cd14643dd78334a00e9fa6923a0c5493
Marian, A (Illinois at Chicago)
Thursday 05 May 2011,...
Marian, A (Illinois at Chicago)
Thursday 05 May 2011, 13:4514:45
Spitalfields Day
Cambridge University
3564
http://sms.cam.ac.uk/media/1137360
Moduli of sheaves and strange duality
Marian, A (Illinois at Chicago)
Thursday 05 May 2011, 13:4514:45
Spitalfields Day
Strange duality is a symmetry that spaces of sections of determinant line bundles over moduli spaces of sheaves are conjectured to obey. I will discuss the conjecture for moduli spaces of sheaves on K3 surfaces. Questions about the geometry of the moduli space of polarized K3s also arise.
20110506T11:29:02+01:00
3564
1137360
true
16x9
false
no

Moduli of Symplectic Maximal Representations
ucs_sms_1087487_1102079
http://sms.cam.ac.uk/media/1102079
Moduli of Symplectic Maximal Representations
Guichard, O (ParisSud 11)
Tuesday 22 February 2011, 10:0011:00
Thu, 24 Feb 2011 13:44:32 +0000
Guichard, O
Steve Greenham
University of Cambridge
Steve Greenham
2d80235871e54831071dd58fd1b25650
f9119578ec824da7fd53e8399820a36d
bc274067d832812cc1019d53cbe65619
Guichard, O (ParisSud 11)
Tuesday 22 February 2011, 10:0011:00
Guichard, O (ParisSud 11)
Tuesday 22 February 2011, 10:0011:00
Cambridge University
4193
http://sms.cam.ac.uk/media/1102079
Moduli of Symplectic Maximal Representations
Guichard, O (ParisSud 11)
Tuesday 22 February 2011, 10:0011:00
Maximal representations of surface groups into symplectic real groups have been extensively studied in the last years. Beautiful results have been obtained using either the algebraic approach offered by the theory of Higgs bundles or a geometric approach based on a formula coming from bounded cohomology. After having recalled those results, we will construct, for a maximal representation ρ:π1(Σg)→Sp(2n,R), an open subset Ω⊂RP2n−1 where π1(Σg) acts properly with compact quotient. The topology of the quotient will then be determined. Finally we shall consider the problem of giving an interpretation of the moduli of maximal symplectic representations as a moduli space of RP2n−1structures and what are the questions that remain to give a complete answer to that problem.
20110224T13:44:38+00:00
4193
1102079
true
16x9
false
no

Moduli space of bundles and Kloosterman sums
ucs_sms_1087487_1137438
http://sms.cam.ac.uk/media/1137438
Moduli space of bundles and Kloosterman sums
Heinloth, J (Amsterdam)
Thursday 05 May 2011, 16:3017:30
Spitalfields Day
Fri, 06 May 2011 12:15:41 +0100
Heinloth, J
Steve Greenham
Isaac Newton Institute
Heinloth, J
711bc20523d69a55d7ffbef1c737ee98
f4e3b09fd720213169a95085e087046a
e3b8380eb668cd928b1481d33e0ab9f3
Heinloth, J (Amsterdam)
Thursday 05 May 2011, 16:3017:30
Spitalfields Day
Heinloth, J (Amsterdam)
Thursday 05 May 2011, 16:3017:30
Spitalfields Day
Cambridge University
3755
http://sms.cam.ac.uk/media/1137438
Moduli space of bundles and Kloosterman sums
Heinloth, J (Amsterdam)
Thursday 05 May 2011, 16:3017:30
Spitalfields Day
The relation between analytic properties of modular forms and arithmetic results has led to many famous results and conjectures. In the geometric analogue of this conjectural relation  called geometric Langlands correspondence quotients of the upper half plane are replaced by moduli spaces of bundles on the curve. We will try to motivate this analogy. Since the geometry of these spaces is complicated in general, very few explicit examples of such modular forms are known. In joint work with B.C. Ngô and Z. Yun  which was motivated by work of Gross and Frenkel  we found an explicit series of such forms which turn out to be closely related to classical Kloosterman sums. This gives an example of the (wild) geometric Langlands correspondence.
20110506T12:15:48+01:00
3755
1137438
true
16x9
false
no

Moduli spaces and physics
ucs_sms_1087487_1088784
http://sms.cam.ac.uk/media/1088784
Moduli spaces and physics
Diaconescu, E (Rutgers)
Friday 07 January 2011, 11:3012:30
Mon, 10 Jan 2011 11:33:40 +0000
Diaconescu, E
Steve Greenham
Isaac Newton Institute
Diaconescu, E
17443eb4a6da952b5e8fbb1c36f50cdc
10924128d260f122e9963733107fb282
a8595671c9a615ad0994b1d5390f979d
Diaconescu, E (Rutgers)
Friday 07 January 2011, 11:3012:30
Diaconescu, E (Rutgers)
Friday 07 January 2011, 11:3012:30
Cambridge University
3838
http://sms.cam.ac.uk/media/1088784
Moduli spaces and physics
Diaconescu, E (Rutgers)
Friday 07 January 2011, 11:3012:30
20110110T11:33:44+00:00
3838
1088784
true
16x9
false
no

Moduli spaces of abelian varieties with Iwahori level structure
ucs_sms_1087487_1105302
http://sms.cam.ac.uk/media/1105302
Moduli spaces of abelian varieties with Iwahori level structure
Goertz , U (Duisberg/Essen)
Thursday 03 March 2011, 14:0015:00
Fri, 04 Mar 2011 10:57:28 +0000
Goertz , U
Steve Greenham
Isaac Newton Institute
Goertz , U
afcf32c31b17f38d9a0176fff83bb738
84139ca9f9fda37b1189c30bf0e8fd72
f00f0dcc6e6c98591591ad6721348186
Goertz , U (Duisberg/Essen)
Thursday 03 March 2011, 14:0015:00
Goertz , U (Duisberg/Essen)
Thursday 03 March 2011, 14:0015:00
Cambridge University
3541
http://sms.cam.ac.uk/media/1105302
Moduli spaces of abelian varieties with Iwahori level structure
Goertz , U (Duisberg/Essen)
Thursday 03 March 2011, 14:0015:00
We discuss moduli spaces of abelian varieties in positive characteristic p, with Iwahori level structure at p. In contrast to the moduli space of principally polarized abelian varieties these spaces are singular and are considerably more complicated. Their local structure can be described quite explicitly in terms of matrix equations. As to the global structure, the most interesting part is the supersingular locus (in other words the unique closed "Newton stratum"), whose structure is closely related to DeligneLusztig varieties.
20110304T10:57:34+00:00
3541
1105302
true
16x9
false
no

Moduli Spaces of Gorenstein QuasiHomogenous Surface Singularities
ucs_sms_1087487_1093933
http://sms.cam.ac.uk/media/1093933
Moduli Spaces of Gorenstein QuasiHomogenous Surface Singularities
Pratoussevitch, A (Liverpool)
Tuesday 25 January 2011, 10.0011.00
Thu, 27 Jan 2011 13:54:33 +0000
Pratoussevitch, A
Steve Greenham
Isaac Newton Institute
Pratoussevitch, A
60912e9c6d31cc6f5ce07177e703af71
815a3ac2cbb43f11c1ad4358963f22f0
c5f504e93d6a895d76e1fbac0c1b51ea
Pratoussevitch, A (Liverpool)
Tuesday 25 January 2011, 10.0011.00
Pratoussevitch, A (Liverpool)
Tuesday 25 January 2011, 10.0011.00
Cambridge University
3651
http://sms.cam.ac.uk/media/1093933
Moduli Spaces of Gorenstein QuasiHomogenous Surface Singularities
Pratoussevitch, A (Liverpool)
Tuesday 25 January 2011, 10.0011.00
Gorenstein quasihomogeneous surface singularities, studied by Dolgachev, Neumann and others, correspond to lifts of Fuchsian groups into the universal covering of PSL(2,R). I will show that the space of Gorenstein quasihomogeneous surface singularities corresponding to a certain Fuchsian group is a finite affine space of Z/mZvalued functions on the Fuchsian group, called mArf functions. Using mArf functions, I will count connected components of the space of Gorenstein quasihomogeneous surface singularities and prove that any connected component is homeomorphic to a quotient of R^d by a discrete group. This work is connected to the earlier results of Atiyah and Mumford on spin structures on compact Riemann surfaces and of Jarvis, Kimura and Vaintrob on moduli spaces of higher spin curves. This is joint work with Sergey Natanzon.
20110127T13:54:38+00:00
3651
1093933
true
16x9
false
no

Moduli spaces of locally homogeneous geometric structures
ucs_sms_1087487_1155097
http://sms.cam.ac.uk/media/1155097
Moduli spaces of locally homogeneous geometric structures
Goldman, W (Maryland)
Friday 01 July 2011, 10:0011:00
Mon, 04 Jul 2011 09:50:04 +0100
Goldman, W
Steve Greenham
Isaac Newton Institute
Goldman, W
a85505bf993c848a41951cecb187f9e6
ca7a26d1d520ad4092fe8f61900c303b
267d74a39c8062bf74d9f6049c50b86a
Goldman, W (Maryland)
Friday 01 July 2011, 10:0011:00
Goldman, W (Maryland)
Friday 01 July 2011, 10:0011:00
Cambridge University
3879
http://sms.cam.ac.uk/media/1155097
Moduli spaces of locally homogeneous geometric structures
Goldman, W (Maryland)
Friday 01 July 2011, 10:0011:00
An Ehresmann structure on a manifold is a geometric structure defined by an atlas of local coordinate charts into a fixed homogeneous space. These structures form deformation spaces which themselves are modeled on the space of representations of the fundamental group. These deformation spaces admit actions of the mapping class group, whose dynamics can be highly nontrivial. In many cases the deformation space embeds inside the space of representations of the fundamental group, and geometric structures provide a powerful tool to study representation spaces of surface groups. This talk will survey several examples of these structures and relate them to other classification problems.
20110704T09:50:13+01:00
3879
1155097
true
16x9
false
no

Monopoles on the product of a surface and the circle
ucs_sms_1087487_1154613
http://sms.cam.ac.uk/media/1154613
Monopoles on the product of a surface and the circle
Hurtubise, J (McGill)
Wednesday 29 June 2011, 11:3012:30
Thu, 30 Jun 2011 09:56:27 +0100
Hurtubise, J
Steve Greenham
Isaac Newton Institute
Hurtubise, J
5e84a441fc549ca4b21ca3e8fa3b2513
2b9ca33fdaeb99df3d50c79ba4c1b0d8
b69e5e59f3662f2b719c167772a7fb80
Hurtubise, J (McGill)
Wednesday 29 June 2011, 11:3012:30
Hurtubise, J (McGill)
Wednesday 29 June 2011, 11:3012:30
Cambridge University
3982
http://sms.cam.ac.uk/media/1154613
Monopoles on the product of a surface and the circle
Hurtubise, J (McGill)
Wednesday 29 June 2011, 11:3012:30
One of the important ingredients of the WittenKapustin approach to the geometric Langlands program is the study of singular monopoles on the product of a Riemann surface and an interval; these mediate Hecke transforms. One special case of this, the selftransforms, corresponds to monopoles on the product of a Riemann surface and a circle. We study the moduli of these, and prove a HitchinKobayashi correspondence. When the surface is a torus, there is in addition an interesting Nahm transform to instantons on the product of a threetorus and the line. (with Benoit Charbonneau).
20110630T09:56:36+01:00
3982
1154613
true
16x9
false
no

Morse theory and the moduli space of flat connections over a nonorientable surface
ucs_sms_1087487_1113785
http://sms.cam.ac.uk/media/1113785
Morse theory and the moduli space of flat connections over a nonorientable surface
Ho, NK (National TsingHua)
Tuesday 08 March 2011, 10:0011:00
Thu, 17 Mar 2011 16:44:38 +0000
Ho, NK
Steve Greenham
Isaac Newton Institute
Ho, NK
0370dce4a7159dcf2b3158ac510f129d
857076ec920345df1255c4da36c2cdde
d53c435248092313f63a7d31eefc5fb7
Ho, NK (National TsingHua)
Tuesday 08 March 2011, 10:0011:00
Ho, NK (National TsingHua)
Tuesday 08 March 2011, 10:0011:00
Cambridge University
4042
http://sms.cam.ac.uk/media/1113785
Morse theory and the moduli space of flat connections over a nonorientable surface
Ho, NK (National TsingHua)
Tuesday 08 March 2011, 10:0011:00
We studied the moduli space of flat connections over a nonorientable surface via a Morse theory approach adapted from Atiyah and Bott's work. We defined a YangMills functional on the space of all connections over a nonorientable surface and obtained a Morse stratification of the space. We defined "super central extension" of the fundamental group of the surface. The representation varieties defined using super central extension correspond to gauge equivariant YangMills connections and enable us to obtain reduction formulas for equivariant strata. To describe the phenomenon of the stratification here, we defined "antiperfect Morse stratification", which is the case when the discrepancy (i.e. the difference between Morse series and Poincare series) reaches its maximal possible value while the perfect Morse stratification is when the discrepancy reaches its minimal possible value zero. This is a joint work with ChiuChu Melissa Liu.
20110317T16:44:44+00:00
4042
1113785
true
16x9
false
no

Motivic DonaldsonThomas theory of the conifold
ucs_sms_1087487_1132322
http://sms.cam.ac.uk/media/1132322
Motivic DonaldsonThomas theory of the conifold
Szendroi, B (Oxford)
Friday 15 April 2011, 14:3015:30
Mon, 18 Apr 2011 12:20:11 +0100
Szendroi, B
Steve Greenham
Isaac Newton Institute
Szendroi, B
5d88609c65e4540c87bdfbe266b094eb
8d5a2b36f0a375fef80bc3ff2c12ba5b
fa9dc658c4fb4f61761ae732699a1c07
Szendroi, B (Oxford)
Friday 15 April 2011, 14:3015:30
Szendroi, B (Oxford)
Friday 15 April 2011, 14:3015:30
Cambridge University
4097
http://sms.cam.ac.uk/media/1132322
Motivic DonaldsonThomas theory of the conifold
Szendroi, B (Oxford)
Friday 15 April 2011, 14:3015:30
The talk will explain the computation of the motivic refinement of DonaldsonThomas theory and related enumerative theories on the resolved conifold geometry, in all chambers of the space of quiver stability conditions. The results are in full agreement with the expected answer from the refined topological vertex of IqbalKozcazVafa, and the wallcrossing computations of JafferisChuang. This is joint work with Andrew Morrison and Kentaro Nagao.
20110418T12:20:19+01:00
4097
1132322
true
16x9
false
no

New results in higher rank BrillNoether theory
ucs_sms_1087487_1147698
http://sms.cam.ac.uk/media/1147698
New results in higher rank BrillNoether theory
Newstead, P (Liverpool)
Thursday 26 May 2011, 16:3017:30
Fri, 03 Jun 2011 16:10:31 +0100
Newstead, P
Steve Greenham
Isaac Newton Institute
Newstead, P
bad4c86f064f6fb250570f13bff8779c
0fab5948beaa4e2628f3254c2041bd97
3bbd7d713fa62abb1a608fbac4cba2e8
Newstead, P (Liverpool)
Thursday 26 May 2011, 16:3017:30
Newstead, P (Liverpool)
Thursday 26 May 2011, 16:3017:30
Cambridge University
4253
http://sms.cam.ac.uk/media/1147698
New results in higher rank BrillNoether theory
Newstead, P (Liverpool)
Thursday 26 May 2011, 16:3017:30
In the last 12 months, many new examples of rank 2 bundles (and some of rank 3 bundles) have been discovered. I will describe briefly the links with Koszul cohomology and the moduli spaces of curves, but most of the talk will be devoted to the construction of the bundles and their relevance to higher rank BrillNoether theory.
20110603T16:10:39+01:00
4253
1147698
true
16x9
false
no

Nodal curves old and new
ucs_sms_1087487_1113977
http://sms.cam.ac.uk/media/1113977
Nodal curves old and new
Thomas, RPW (Imperial)
Friday 11 March 2011, 15:1516:15
Fri, 18 Mar 2011 10:07:41 +0000
Thomas, RPW
Steve Greenham
Isaac Newton Institute
Thomas, RPW
ebf04db19019ed990785f966b6eda3e9
78e8c4b867624c4f5c68ca3d034cd511
3703dd0da187fbf4f5600ae12da07f96
Thomas, RPW (Imperial)
Friday 11 March 2011, 15:1516:15
Thomas, RPW (Imperial)
Friday 11 March 2011, 15:1516:15
Cambridge University
3581
http://sms.cam.ac.uk/media/1113977
Nodal curves old and new
Thomas, RPW (Imperial)
Friday 11 March 2011, 15:1516:15
I will describe a classical problem going back to 1848 (Steiner, Cayley, Salmon,...) and a solution using simple techniques, but techniques that one would never really have thought of without ideas coming from string theory (GromovWitten invariants, BPS states) and modern geometry (the MaulikNekrasovOkounkovPandharipande conjecture). In generic families of curves C on a complex surface S, nodal curves  those with the simplest possible singularities  appear in codimension 1. More generally those with d nodes occur in codimension d. In particular a ddimensional linear family of curves should contain a finite number of such dnodal curves. The classical problem  at least in the case of S being the projective plane  is to determine this number. The Göttsche conjecture states that the answer should be topological, given by a universal degree d polynomial in the four numbers C.C, c_1(S).C, c_1(S)^2 and c_2(S). There are now proofs in various settings; a completely algebraic proof was found recently by Tzeng. I will explain a simpler approach which is joint work with Martijn Kool and Vivek Shende.
20110318T10:07:47+00:00
3581
1113977
true
16x9
false
no

On simple finite subgroups in the Cremona group of rank 3
ucs_sms_1087487_1147632
http://sms.cam.ac.uk/media/1147632
On simple finite subgroups in the Cremona group of rank 3
Cheltsov, I (Edinburgh)
Tuesday 24 May 2011, 15:3016:30
Fri, 03 Jun 2011 15:13:33 +0100
Cheltsov, I
Steve Greenham
Isaac Newton Institute
Cheltsov, I
4999990d172adbb31277994788fffa06
5267a9d54f0a6d307c9b05e58e268178
f22d53ce7b671cb203782e767d5f5088
Cheltsov, I (Edinburgh)
Tuesday 24 May 2011, 15:3016:30
Cheltsov, I (Edinburgh)
Tuesday 24 May 2011, 15:3016:30
Cambridge University
3888
http://sms.cam.ac.uk/media/1147632
On simple finite subgroups in the Cremona group of rank 3
Cheltsov, I (Edinburgh)
Tuesday 24 May 2011, 15:3016:30
The Cremona group of rank N is the group of birational selfmaps of the projective space of dimension N. Recently Yura Prokhorov (Moscow) classified all finite simple subgroups in the Cremona group of rank 3 (this answers a question of Serre). I will show how to apply NadelShokurov vanishing and Kawamata subadjunction to study conjugacy classes of the subgroups classified by Prokhorov. In particular, I give a partial answer to another question of Serre on normalizers of finite simple subgroups in the Cremona of rank 3. This is a joint work with Costya Shramov (Moscow).
20110603T15:13:42+01:00
3888
1147632
true
16x9
false
no

On the Calculus underlying DonaldsonThomas theory
ucs_sms_1087487_1094301
http://sms.cam.ac.uk/media/1094301
On the Calculus underlying DonaldsonThomas theory
Behrend, KB (University of British Columbia)
Thursday 27 January 2011, 15:3016:30
Mon, 31 Jan 2011 09:46:46 +0000
Behrend, KB
Steve Greenham
Isaac Newton Institute
Behrend, KB
6595b47d6e8c9cdd0628322f37bd5ccb
e8e44aa9ffdd0bacab748db13332bfe7
3b5a875ce0bd4356b5a93d8e8123b747
Behrend, KB (University of British Columbia)
Thursday 27 January 2011,...
Behrend, KB (University of British Columbia)
Thursday 27 January 2011, 15:3016:30
Cambridge University
3804
http://sms.cam.ac.uk/media/1094301
On the Calculus underlying DonaldsonThomas theory
Behrend, KB (University of British Columbia)
Thursday 27 January 2011, 15:3016:30
On a manifold there is the graded algebra of polyvector fields with its LieSchouten bracket, and the module of de Rham differentials with exteriour differentiation. This package is called a "calculus". The moduli space of sheaves (or derived category objects) on a CalabiYau threefold has a kind of "virtual calculus" on it. In particular, this moduli space has virtual de Rham cohomology groups, which categorify DonaldsonThomas invariants, at least conjecturally. We describe some attempts at constructing such a virtual calculus. This is work in progress.
20110131T09:46:51+00:00
3804
1094301
true
16x9
false
no

On the modular interpretation of the NagarajSeshadri locus
ucs_sms_1087487_1147682
http://sms.cam.ac.uk/media/1147682
On the modular interpretation of the NagarajSeshadri locus
Schmitt, A (Free University of Berlin)
Thursday 26 May 2011, 15:1516:15
Fri, 03 Jun 2011 15:55:37 +0100
Schmitt, A
Steve Greenham
Isaac Newton Institute
Schmitt, A
304b02431af595cf9631afdbc2b73a56
013ab9c9f50a67cf10fcb27c86ae1371
de9e9553d2cce1700eac198ee4f982a3
Schmitt, A (Free University of Berlin)
Thursday 26 May 2011, 15:1516:15
Schmitt, A (Free University of Berlin)
Thursday 26 May 2011, 15:1516:15
Cambridge University
3842
http://sms.cam.ac.uk/media/1147682
On the modular interpretation of the NagarajSeshadri locus
Schmitt, A (Free University of Berlin)
Thursday 26 May 2011, 15:1516:15
We will survey constructions of moduli spaces for principal bundles on nodal curves over the complex numbers. This includes a moduli space for torsion free sheaves A of rank r and degree zero on an irreducible nodal curve X which are endowed with a homomorphism d: ∧^r A → O_X which is an isomorphism away from the node. It is a degeneration of the moduli space of SL_r(C)bundles on a smooth curve. In many cases, this moduli space puts a scheme structure on the "NagarajSeshadri locus" inside the moduli space of semistable torsion free sheaves of rank r and degree zero.
20110603T15:55:46+01:00
3842
1147682
true
16x9
false
no

On the monodromy of the Hitchin connection
ucs_sms_1087487_1105204
http://sms.cam.ac.uk/media/1105204
On the monodromy of the Hitchin connection
Pauly, C (Montpellier 2)
Thursday 24 February 2011, 14:0015:00
Fri, 04 Mar 2011 10:23:07 +0000
Pauly, C
Steve Greenham
Isaac Newton Institute
Pauly, C
f9be1df1dd43dac782b4a75a6694ec30
c1fca2914e9fc951c56998a73569b58f
a24de2a8ee304ea72da0e7c6ec053f43
Pauly, C (Montpellier 2)
Thursday 24 February 2011, 14:0015:00
Pauly, C (Montpellier 2)
Thursday 24 February 2011, 14:0015:00
Cambridge University
4482
http://sms.cam.ac.uk/media/1105204
On the monodromy of the Hitchin connection
Pauly, C (Montpellier 2)
Thursday 24 February 2011, 14:0015:00
In this talk I will show that the monodromy representation of the projective Hitchin connection on the sheaf of generalized theta functions on the moduli space of vector bundles over a curve has an element of infinite order in its image. I will explain the link with conformal blocks.
20110304T10:23:13+00:00
4482
1105204
true
16x9
false
no

On the motivic class of the commuting variety and related problems
ucs_sms_1087487_1132304
http://sms.cam.ac.uk/media/1132304
On the motivic class of the commuting variety and related problems
Bryan, J (British Columbia)
Friday 15 April 2011, 11:0012:00
Mon, 18 Apr 2011 12:08:59 +0100
Bryan, J
Steve Greenham
Isaac Newton Institute
Bryan, J
60e3b417115ea0d5e4de955848cf2eec
cf8f511e79c029766a13fa6f610e2d60
0d5f6222c6430e40c3afcb9b2fafa943
Bryan, J (British Columbia)
Friday 15 April 2011, 11:0012:00
Bryan, J (British Columbia)
Friday 15 April 2011, 11:0012:00
Cambridge University
3805
http://sms.cam.ac.uk/media/1132304
On the motivic class of the commuting variety and related problems
Bryan, J (British Columbia)
Friday 15 April 2011, 11:0012:00
In 1960, Feit and Fine found a beautiful formula for the number of commuting n by n matrices over the finite field F_q. Their result can be reinterpreted as a formula for the motivic class of the commuting variety in the Grothendieck group. We will describe a simple new proof of their formula which allows us to generalize the result to several other settings with applications to motivic DonaldsonThomas theory.
20110418T12:09:07+01:00
3805
1132304
true
16x9
false
no

On the singularities of moduli spaces of principal bundles
ucs_sms_1087487_1102001
http://sms.cam.ac.uk/media/1102001
On the singularities of moduli spaces of principal bundles
Serman, O (Université des Sciences et Technologies de Lille)
Tuesday 15 February 2011, 11:3012:30
Thu, 24 Feb 2011 12:50:18 +0000
Serman, O
Steve Greenham
Isaac Newton Institute
Serman, O
351c032527f354e82a783aa1734904dd
659afdbf10e3ec8d5c27707562d2f603
fcf563a6204fd6dbe60be7898b1fb10a
Serman, O (Université des Sciences et Technologies de Lille)
Tuesday 15...
Serman, O (Université des Sciences et Technologies de Lille)
Tuesday 15 February 2011, 11:3012:30
Cambridge University
3608
http://sms.cam.ac.uk/media/1102001
On the singularities of moduli spaces of principal bundles
Serman, O (Université des Sciences et Technologies de Lille)
Tuesday 15 February 2011, 11:3012:30
We show how local factoriality of GIT quotients can be used to give a description of the singular locus of moduli spaces of principal bundles on curves. We then compute the fundamental group of the smooth locus of these moduli spaces.
20110224T12:50:23+00:00
3608
1102001
true
16x9
false
no

Orthogonal and symplectic parabolic bundles
ucs_sms_1087487_1147723
http://sms.cam.ac.uk/media/1147723
Orthogonal and symplectic parabolic bundles
Biswas, I (TIFR)
Tuesday 31 May 2011, 10:0011:00
Fri, 03 Jun 2011 16:23:43 +0100
Biswas, I
Steve Greenham
Isaac Newton Institute
Biswas, I
382839704355765371a7b6a40843fbd0
bf602ede91a8ebcc9c4664bced198076
3604a4dd246648bee628d1d67267d01b
Biswas, I (TIFR)
Tuesday 31 May 2011, 10:0011:00
Biswas, I (TIFR)
Tuesday 31 May 2011, 10:0011:00
Cambridge University
3685
http://sms.cam.ac.uk/media/1147723
Orthogonal and symplectic parabolic bundles
Biswas, I (TIFR)
Tuesday 31 May 2011, 10:0011:00
In this work with S. Majumder and M. L. Wong, we investigate orthogonal and symplectic bundles, with parabolic structure, over a curve.
20110603T16:23:51+01:00
3685
1147723
true
16x9
false
no

Parahoric bundles and parabolic bundles
ucs_sms_1087487_1101932
http://sms.cam.ac.uk/media/1101932
Parahoric bundles and parabolic bundles
Balaji, V (Chennai Mathematical Institute)
Tuesday 15 February 2011, 10:0011:00
Thu, 24 Feb 2011 12:28:58 +0000
Balaji, V
Steve Greenham
Isaac Newton Institute
Balaji, V
dd39dac3db480320bac23d1ddca4b36b
abaefebff56a6c8e8aba31256ba5e6c0
a77ffa9c1fdb384f9e93797cc2db4ecd
Balaji, V (Chennai Mathematical Institute)
Tuesday 15 February 2011,...
Balaji, V (Chennai Mathematical Institute)
Tuesday 15 February 2011, 10:0011:00
Cambridge University
4150
http://sms.cam.ac.uk/media/1101932
Parahoric bundles and parabolic bundles
Balaji, V (Chennai Mathematical Institute)
Tuesday 15 February 2011, 10:0011:00
Let X be a compact Riemann surface of genus g≥2 and let G be a semisimple simply connected algebraic group. We introduce the notion of a {\em parahoric} Gbundle or equivalently a torsor under a suitable BruhatTits group scheme. We also construct the moduli space of semistable parahoric Gbundles and identify the underlying topological space of this moduli space with certain spaces of homomorphisms of Fuchsian groups into maximal compact subgroup of G. These results generalize the earlier results of Mehta and Seshadri on parabolic vector bundles. (joint work with C.S Seshadri).
20110224T12:29:03+00:00
4150
1101932
true
16x9
false
no

Partially positive line bundles
ucs_sms_1087487_1147581
http://sms.cam.ac.uk/media/1147581
Partially positive line bundles
Totaro, B (DPMMS, Cambridge)
Thursday 12 May 2011, 10:3011:30
Fri, 03 Jun 2011 14:37:11 +0100
Totaro, B
Steve Greenham
Isaac Newton Institute
Totaro, B
1f7b2926c9421aa9f19d1910ac979273
9414eda94a6563ce9f6818728f63e690
61950a2d1f3af4dc798acb94ca97343c
Totaro, B (DPMMS, Cambridge)
Thursday 12 May 2011, 10:3011:30
Totaro, B (DPMMS, Cambridge)
Thursday 12 May 2011, 10:3011:30
Cambridge University
2532
http://sms.cam.ac.uk/media/1147581
Partially positive line bundles
Totaro, B (DPMMS, Cambridge)
Thursday 12 May 2011, 10:3011:30
Define a line bundle L on a projective variety to be qample, for a natural number q, if tensoring with high powers of L kills coherent sheaf cohomology above dimension q. Thus 0ampleness is the usual notion of ampleness. Intuitively, a line bundle is qample if it is positive "in all but at most q directions". We prove some of the basic properties of qample line bundles. Related ideas have been used by Ottem to define what an "ample subvariety" of any codimension should mean.
20110603T14:37:19+01:00
2532
1147581
true
16x9
false
no

Poincare families and line bundles on moduli stacks of Gbundles
ucs_sms_1087487_1095934
http://sms.cam.ac.uk/media/1095934
Poincare families and line bundles on moduli stacks of Gbundles
Hoffmann, N (Freie Universität Berlin)
Tuesday 01 February 2011, 10:0011:00
Tue, 08 Feb 2011 13:05:05 +0000
Hoffmann, N
Steve Greenham
Isaac Newton Institute
Hoffmann, N
6bfa805902ee329041a742b177532941
e9dc65cc1569080b13ce0dcd74aca079
06d8c3d6ae81d8b0615360ffb4fd3042
Hoffmann, N (Freie Universität Berlin)
Tuesday 01 February 2011, 10:0011:00
Hoffmann, N (Freie Universität Berlin)
Tuesday 01 February 2011, 10:0011:00
Cambridge University
3874
http://sms.cam.ac.uk/media/1095934
Poincare families and line bundles on moduli stacks of Gbundles
Hoffmann, N (Freie Universität Berlin)
Tuesday 01 February 2011, 10:0011:00
The talk deals with the following question: Which moduli spaces of principal Gbundles over a smooth projective curve carry Poincare families (or universal families)? The obstruction is the Brauer class of the moduli stack as a gerbe over the coarse moduli scheme. This obstruction is described in terms of the root system of G. The proof uses the Picard group of the moduli stack. This is joint work with I. Biswas.
20110208T13:05:11+00:00
3874
1095934
true
16x9
false
no

Poisson modules
ucs_sms_1087487_1113958
http://sms.cam.ac.uk/media/1113958
Poisson modules
Hitchin, N (Oxford)
Friday 11 March 2011, 14:0015:00
Fri, 18 Mar 2011 09:53:49 +0000
Hitchin, N
Steve Greenham
Isaac Newton Institute
Hitchin, N
d31ec8da1f40551363bf2ebcdc11709b
caf20ace8c13728271fdcb67b628d0e6
14de6c554ace85933bb3939225f7ee56
Hitchin, N (Oxford)
Friday 11 March 2011, 14:0015:00
Hitchin, N (Oxford)
Friday 11 March 2011, 14:0015:00
Cambridge University
3812
http://sms.cam.ac.uk/media/1113958
Poisson modules
Hitchin, N (Oxford)
Friday 11 March 2011, 14:0015:00
Within the context of holomorphic Poisson geometry, there is a natural notion of a Poisson module, which is a holomorphic vector bundle with additional structure. For a symplectic structure, this is just a flat connection, but for a general Poisson structure there are a number of constructions and examples which we shall describe. Even the case of the zero Poisson structure is nontrivial as it leads to the notion of coHiggs bundles.
20110318T09:53:56+00:00
3812
1113958
true
16x9
false
no

Postnikov stability for complexes
ucs_sms_1087487_1126677
http://sms.cam.ac.uk/media/1126677
Postnikov stability for complexes
Ploog, D (Leibniz)
Thursday 07 April 2011, 11:3012:30
Mon, 11 Apr 2011 14:33:19 +0100
Ploog, D
Steve Greenham
Isaac Newton Institute
Ploog, D
ef540191f905dfdda7f478a1d949ec9f
b1648e8acffc7864ff56544cb5e36b04
48e345924458dc5c73988f0ce2fa10d0
Ploog, D (Leibniz)
Thursday 07 April 2011, 11:3012:30
Ploog, D (Leibniz)
Thursday 07 April 2011, 11:3012:30
Cambridge University
3556
http://sms.cam.ac.uk/media/1126677
Postnikov stability for complexes
Ploog, D (Leibniz)
Thursday 07 April 2011, 11:3012:30
There are several approaches for extending (semi)stability from sheaves to complexes, or rather triangulated categories. In work with Georg Hein (arXiv 0704.2512, 0901.1554), we have introduced a notion of "Postnikov stability" for general triangulated categories, the motivation being Falting's observation that semistability of vector bundles on smooth, projective curves is characterised by the existence of orthogonal sheaves. Our main result is that for projective varieties, classical stability of sheaves can always be captured by an appropriate Postnikov stability. Some applications of this theory: compactifications of classical moduli spaces using genuine complexes; a more conceptual look on questions around "preservation of stability"; answer to a conjecture of Friedman on stable sheaves on elliptic surfaces (the latter is Bernadara/Hein, 1002.4986).
20110411T14:33:28+01:00
3556
1126677
true
16x9
false
no

Principal bundles  I
ucs_sms_1087487_1087610
http://sms.cam.ac.uk/media/1087610
Principal bundles  I
Gómez, T (Universidad Complutense de Madrid)
Wednesday 05 January 2011, 11:3012:30
Thu, 06 Jan 2011 09:22:25 +0000
Gómez, T
Steve Greenham
Isaac Newton Institute
Gómez, T
c1c2008ef4571f3e2e8f6fb9661af34f
de56ade4b237aa76867cb0659d955415
8ea5bc8d269f727134e153afc10fb171
Gómez, T (Universidad Complutense de Madrid)
Wednesday 05 January 2011,...
Gómez, T (Universidad Complutense de Madrid)
Wednesday 05 January 2011, 11:3012:30
Cambridge University
3531
http://sms.cam.ac.uk/media/1087610
Principal bundles  I
Gómez, T (Universidad Complutense de Madrid)
Wednesday 05 January 2011, 11:3012:30
This is an introduction to principal bundles in algebraic geometry. We will start with the basic definitions (associated fibrations, reduction and extension of structure group, stability, etc...) and then give a sketch of the construction of the moduli.
Notes: The following are the notes of some lectures I gave in Warsaw. In that school I gave 5 lectures, so this time I won't be able to cover all this material, but this could serve as a reference: T. Gomez, Lectures on principal bundles over projective varieties, Pragacz, P. (Ed.) Algebraic cycles, sheaves, shtukas, and moduli. Impanga lecture notes. Trends in Mathematics. Birkh\"auser Verlag, Basel, 2008. viii+236 pp., 4568. Lectures on Principal Bundles over proyective varieties. arXiv: 1011.1801v1
20110106T09:22:30+00:00
3531
1087610
true
16x9
false
no

Principal bundles  II
ucs_sms_1087487_1087976
http://sms.cam.ac.uk/media/1087976
Principal bundles  II
Gómez, T (Universidad Complutense de Madrid)
Thursday 06 January 2011, 11:3012:30
Thu, 06 Jan 2011 17:26:16 +0000
Gómez, T
Steve Greenham
Isaac Newton Institute
Gómez, T
4cb8fbd64cc1d6991767b04ab7307f08
da5b9eb5d531dedf03c6d2587c2a6c57
751077bd7c3b5c965b31c9b537027d47
Gómez, T (Universidad Complutense de Madrid)
Thursday 06 January 2011,...
Gómez, T (Universidad Complutense de Madrid)
Thursday 06 January 2011, 11:3012:30
Cambridge University
3958
http://sms.cam.ac.uk/media/1087976
Principal bundles  II
Gómez, T (Universidad Complutense de Madrid)
Thursday 06 January 2011, 11:3012:30
This is an introduction to principal bundles in algebraic geometry. We will start with the basic definitions (associated fibrations, reduction and extension of structure group, stability, etc...) and then give a sketch of the construction of the moduli.
Notes: The following are the notes of some lectures I gave in Warsaw. In that school I gave 5 lectures, so this time I won't be able to cover all this material, but this could serve as a reference: T. Gomez, Lectures on principal bundles over projective varieties, Pragacz, P. (Ed.) Algebraic cycles, sheaves, shtukas, and moduli. Impanga lecture notes. Trends in Mathematics. Birkh\"auser Verlag, Basel, 2008. viii+236 pp., 4568. Lectures on Principal Bundles over proyective varieties. arXiv: 1011.1801v1
20110106T17:26:20+00:00
3958
1087976
true
16x9
false
no

Quadratic differentials as stability conditions
ucs_sms_1087487_1126520
http://sms.cam.ac.uk/media/1126520
Quadratic differentials as stability conditions
Smith, I (Cambridge)
Tuesday 05 April 2011, 11:3012:30
Mon, 11 Apr 2011 13:12:08 +0100
Smith, I
Steve Greenham
Isaac Newton Institute
Smith, I
b085b493f6725e18efba3e8c0edf6bbe
724c8c2b54b20e18030fc9b5cc23288e
212154489a7e4689702fcbdc6f4bd608
Smith, I (Cambridge)
Tuesday 05 April 2011, 11:3012:30
Smith, I (Cambridge)
Tuesday 05 April 2011, 11:3012:30
Cambridge University
3878
http://sms.cam.ac.uk/media/1126520
Quadratic differentials as stability conditions
Smith, I (Cambridge)
Tuesday 05 April 2011, 11:3012:30
I will explain how certain moduli spaces of meromorphic quadratic differentials arising in Teichmuller theory are related to spaces of stability conditions on the Fukaya categories of some particular quasiprojective CalabiYau 3folds. These Fukaya categories can be described via Ginzburg algebras associated to quivers defined by triangulations of a Riemann surface; suitable triangulations are obtained from the foliations defined by generic quadratic differentials. This is joint work with Tom Bridgeland.
20110411T13:12:15+01:00
3878
1126520
true
16x9
false
no

Quiver varieties and tensor products
ucs_sms_1087487_1131618
http://sms.cam.ac.uk/media/1131618
Quiver varieties and tensor products
Nakajima, H (Kyoto)
Monday 11 April 2011, 15:0016:00
Fri, 15 Apr 2011 13:06:03 +0100
Nakajima, H
Steve Greenham
Isaac Newton Institute
Nakajima, H
d3f3961a6c172e891a423ec6c5537148
8e74169e380d74e44e0a453b635990b0
f5284a845b557fd1247fcde4b8a9018b
Nakajima, H (Kyoto)
Monday 11 April 2011, 15:0016:00
Nakajima, H (Kyoto)
Monday 11 April 2011, 15:0016:00
Cambridge University
4179
http://sms.cam.ac.uk/media/1131618
Quiver varieties and tensor products
Nakajima, H (Kyoto)
Monday 11 April 2011, 15:0016:00
I will explain how tensor products of representations of Yangian are realized in terms of geometry of quiver varieties.
20110415T13:06:10+01:00
4179
1131618
true
16x9
false
no

Rank two BrillNoether theory and the birational geometry of the moduli space of curves
ucs_sms_1087487_1154576
http://sms.cam.ac.uk/media/1154576
Rank two BrillNoether theory and the birational geometry of the moduli space of curves
Farkas, G (Humboldt)
Tuesday 28 June 2011, 16:3017:30
Thu, 30 Jun 2011 09:30:00 +0100
Farkas, G
Steve Greenham
Isaac Newton Institute
Farkas, G
428c4404626e246cddf4f436d777d244
42c637a85fdfd794ce0962806bb4493b
b1096aaa5e3e3dacf1fc1e5f63ac155c
Farkas, G (Humboldt)
Tuesday 28 June 2011, 16:3017:30
Farkas, G (Humboldt)
Tuesday 28 June 2011, 16:3017:30
Cambridge University
3991
http://sms.cam.ac.uk/media/1154576
Rank two BrillNoether theory and the birational geometry of the moduli space of curves
Farkas, G (Humboldt)
Tuesday 28 June 2011, 16:3017:30
I shall discuss applications of Koszul cohomology and rank two BrillNoether theory to the intersection theory of the moduli space of curves. For instance, one can construct extremal divisors in M_g whose points are characterized in terms of existence of certain rank two vector bundles. I shall then explain how these subvarieties of M_g can be thought of as failure loci of an interesting prediction of Mercat in higher rank BrillNoether theory.
20110630T09:30:09+01:00
3991
1154576
true
16x9
false
no

Refined curve counting on algebraic surfaces
ucs_sms_1087487_1154414
http://sms.cam.ac.uk/media/1154414
Refined curve counting on algebraic surfaces
Goettsche, L (ICTP)
Monday 27 June 2011, 16:3017:30
Wed, 29 Jun 2011 16:37:21 +0100
Goettsche, L
Steve Greenham
Isaac Newton Institute
Goettsche, L
0b0224d3a2cbc86bd7496ab0d2ad3fdc
a7f580403649a9c702260f39b374d6aa
a5d7c7cf0b4023d359dca5e9d8d5a939
Goettsche, L (ICTP)
Monday 27 June 2011, 16:3017:30
Goettsche, L (ICTP)
Monday 27 June 2011, 16:3017:30
Cambridge University
3721
http://sms.cam.ac.uk/media/1154414
Refined curve counting on algebraic surfaces
Goettsche, L (ICTP)
Monday 27 June 2011, 16:3017:30
Let L be ample line bundle on an an algebraic surface X. If L is sufficiently ample wrt d, the number td(L) of dnodal curves in a general ddimensional sub linear system of L will be finite. KoolShendeThomas use the generating function of the Euler numbers of the relative Hilbert schemes of points of the universal curve over L to define the numbers td(L) as BPS invariants and prove a conjecture of mine about their generating function (proved by Tzeng using different methods).
We use the generating function of the χygenera of these relative Hilbert schemes to define and study refined curve counting invariants, which instead of numbers are now polynomials in y, specializing to the numbers of curves for y=1. If X is a K3 surface we relate these invariants to the DonaldsonThomas invariants considered by MaulikPandharipandeThomas.
In the case of toric surfaces we find that the refined invariants interpolate between the GromowWitten invariants (at y=1) and the Welschinger invariants at y=−1. We also find that refined invariants of toric surfaces can be defined and computed by a CaporasoHarris type recursion, which specializes (at y=1,−1) to the corresponding recursion for complex curves and the Welschinger invariants. This is in part joint work with Vivek Shende.
20110629T16:37:29+01:00
3721
1154414
true
16x9
false
no

Relative FourierMukai transforms for Weierstrass fibrations, abelian schemes and Fano fibrations
ucs_sms_1087487_1093913
http://sms.cam.ac.uk/media/1093913
Relative FourierMukai transforms for Weierstrass fibrations, abelian schemes and Fano fibrations
Lopez Martin, C (Salamanca)
Thursday 20 January 2011, 15:3016:30
Thu, 27 Jan 2011 13:31:58 +0000
Lopez Martin, C
Steve Greenham
Isaac Newton Institute
Lopez Martin, C
7793749758a702e5c500746550533ddd
7588c27c764cc2a28a732e126b15b968
9b086e42f2bbe2a816d0e2ee7b055ce9
Lopez Martin, C (Salamanca)
Thursday 20 January 2011, 15:3016:30
Lopez Martin, C (Salamanca)
Thursday 20 January 2011, 15:3016:30
Cambridge University
3902
http://sms.cam.ac.uk/media/1093913
Relative FourierMukai transforms for Weierstrass fibrations, abelian schemes and Fano fibrations
Lopez Martin, C (Salamanca)
Thursday 20 January 2011, 15:3016:30
Since its introduction by Mukai, the theory of integral functors and FourierMukai transforms have been important tools in the study of the geometry of varieties and moduli spaces.
Working with a fibered scheme over a base T it is quite natural to look at the group of Tlinear autoequivalences. The description of this group seems a hard problem. We will restrict ourselves to the subgroup given by relative FourierMukai transforms. In this talk, I will explain how for a projective fibration the knowledge of the structure of the group of autoequivalences of its fibres and the properties of relative integral functors provide a machinery to study that subgroup. I will work out the case of a Weierstrass fibrations and report about the results for abelian schemes and Fano or antiFano fibrations.
20110127T13:32:03+00:00
3902
1093913
true
16x9
false
no

Relative spherical objects and spherical fibrations
ucs_sms_1087487_1126699
http://sms.cam.ac.uk/media/1126699
Relative spherical objects and spherical fibrations
Logvinenko, T (Warwick)
Thursday 07 April 2011, 16:3017:30
Mon, 11 Apr 2011 14:54:19 +0100
Logvinenko, T
Steve Greenham
Isaac Newton Institute
Logvinenko, T
c4884270c46f9d4e6a095811d9de71f3
38a7df4cac959c16308417baae1515fd
419ae4cb25df61f909b2e1009772a0b0
Logvinenko, T (Warwick)
Thursday 07 April 2011, 16:3017:30
Logvinenko, T (Warwick)
Thursday 07 April 2011, 16:3017:30
Cambridge University
3906
http://sms.cam.ac.uk/media/1126699
Relative spherical objects and spherical fibrations
Logvinenko, T (Warwick)
Thursday 07 April 2011, 16:3017:30
Seidel and Thomas introduced some years ago a notion of a spherical object in the derived category D(X) of a smooth projective variety X. We introduce a relative analogue of this notion by defining what does it mean for an object E of the derived category D(Z x X) of a fiber product of two schemes Z and X to be spherical over Z. For objects of D(Z x X) which are orthogonal over Z (these are categorical equivalents of a subscheme of X fibered over Z) we show an object to be spherical over Z if and only if it possesses certain cohomological properties similar to those in the original definition by Seidel and Thomas. We then interpret this geometrically for the special case where our objects are actual flat subschemes of X flatly fibered over Y. This is a joint work with Rina Anno of UChicago."
20110411T14:54:27+01:00
3906
1126699
true
16x9
false
no

Representations of surface groups and Higgs bundles  I
ucs_sms_1087487_1088764
http://sms.cam.ac.uk/media/1088764
Representations of surface groups and Higgs bundles  I
Gothen, P (Universidade do Porto)
Friday 07 January 2011, 10:0011:00
Mon, 10 Jan 2011 11:17:20 +0000
Gothen, P
Steve Greenham
Isaac Newton Institute
Gothen, P
da4a0f663861ed94374a24195be89bb1
489ceb38346060d697e2d84933058860
91eb2328140e7ef268496f204297d6b7
Gothen, P (Universidade do Porto)
Friday 07 January 2011, 10:0011:00
Gothen, P (Universidade do Porto)
Friday 07 January 2011, 10:0011:00
Cambridge University
3973
http://sms.cam.ac.uk/media/1088764
Representations of surface groups and Higgs bundles  I
Gothen, P (Universidade do Porto)
Friday 07 January 2011, 10:0011:00
Classical Hodge theory uses harmonic forms as preferred representatives of cohomology classes. A representation of the fundamental group of a Riemann surface gives rise to a corresponding flat bundle. A Theorem of Donaldson and Corlette shows how to find a harmonic metric in this bundle. A flat bundle corresponds to class in first nonabelian cohomology and the Theorem can be viewed as an analogue of the classical representation of de Rham cohomology classes by harmonic forms.
20110111T17:32:16+00:00
3973
1088764
true
16x9
false
no

Representations of surface groups and Higgs bundles  II
ucs_sms_1087487_1090973
http://sms.cam.ac.uk/media/1090973
Representations of surface groups and Higgs bundles  II
Gothen, P (Universidade do Porto)
Monday 10 January 2011, 11:3012:30
Thu, 13 Jan 2011 09:36:39 +0000
Gothen, P
Tim Cooper
Isaac Newton Institute
Gothen, P
928d2b95a74b431e090dc9af9c4f2185
03cf76c805a1912a635f32dd97ea2e8b
4a295cbe47a076ed83756ccdbb5ae0cf
0cfebaa2cddd2867f7ebeaf3e174bc49
bf6803351449142626785a4a18b48271
Gothen, P (Universidade do Porto)
Monday 10 January 2011, 11:3012:30
Gothen, P (Universidade do Porto)
Monday 10 January 2011, 11:3012:30
Cambridge University
3758
http://sms.cam.ac.uk/media/1090973
Representations of surface groups and Higgs bundles  II
Gothen, P (Universidade do Porto)
Monday 10 January 2011, 11:3012:30
A Higgs bundle on a Riemann surface is a pair consisting of a holomorphic bundle and a holomorphic oneform, the Higgs field, with values in a certain associated vector bundle. A theorem of Hitchin and Simpson says that a stable Higgs bundle admits a metric satisfying Hitchin's equations. Together with the Theorem of Corlette and Donaldson, the HitchinKobayashi correspondence generalizes the classical Hodge decomposition of the first cohomology of the Riemann surface, providing a correspondence between isomorphism classes of Higgs bundles and representations of the fundamental group of the surface.
20110113T09:36:44+00:00
3758
1090973
true
4x3
false
no

Representations of surface groups and Higgs bundles  III
ucs_sms_1087487_1091120
http://sms.cam.ac.uk/media/1091120
Representations of surface groups and Higgs bundles  III
Gothen, P (Universidade do Porto)
Tuesday 11 January 2011, 11:3012:30
Thu, 13 Jan 2011 15:25:22 +0000
Gothen, P
Tim Cooper
Isaac Newton Institute
Gothen, P
87aae9e72280d31f9b3a5b960808d120
bc8317513357923f786f4a7813931bf2
cd12c861a84f3d97b8ed6aad77446384
8c55e1a5d8c47259f325d84465a14914
1ada16c7ab0eb3b23590548966dacbf5
Gothen, P (Universidade do Porto)
Tuesday 11 January 2011, 11:3012:30
Gothen, P (Universidade do Porto)
Tuesday 11 January 2011, 11:3012:30
Cambridge University
3788
http://sms.cam.ac.uk/media/1091120
Representations of surface groups and Higgs bundles  III
Gothen, P (Universidade do Porto)
Tuesday 11 January 2011, 11:3012:30
In the final lecture, we give some applications of Higgs bundle theory to the study of the geometry and topology of character varieties for surface groups, via the identification with moduli of Higgs bundles.
20110113T15:25:27+00:00
3788
1091120
true
4x3
false
no

Representations of the fundamental group and geometric loci of bundles
ucs_sms_1087487_1147666
http://sms.cam.ac.uk/media/1147666
Representations of the fundamental group and geometric loci of bundles
Ramanan, S (Chennai)
Thursday 26 May 2011, 13:4514:45
Fri, 03 Jun 2011 15:43:47 +0100
Ramanan, S
Steve Greenham
Isaac Newton Institute
Ramanan, S
bef9480d250c0571abacfb9bc2f050d3
d8866277bd90d1ad14779b733f3c1a5b
c06bac6e262a87bbb98f0788a4a7167d
Ramanan, S (Chennai)
Thursday 26 May 2011, 13:4514:45
Ramanan, S (Chennai)
Thursday 26 May 2011, 13:4514:45
Cambridge University
4066
http://sms.cam.ac.uk/media/1147666
Representations of the fundamental group and geometric loci of bundles
Ramanan, S (Chennai)
Thursday 26 May 2011, 13:4514:45
Starting with Weil's seminal work on vector bundles, the relation between representations of the fundamental group and vector bundles have been studied from various points of view. The work of Narasimhan and Seshadri made clear the relation of unitary representations to polystable bundles. One of Nigel Hitchin's results pertains to representations into the split real forms of semisimple groups. I will be giving an overview of these ending up with my effort, in collaboration with Oscar GarciaPrada, to understand these as relating to fixed point varieties under some natural involutions on the moduli of Higgs pairs.
20110603T15:43:55+01:00
4066
1147666
true
16x9
false
no

Ribbon Graphs and Mirror Symmetry
ucs_sms_1087487_1132205
http://sms.cam.ac.uk/media/1132205
Ribbon Graphs and Mirror Symmetry
Zaslow, E (Northwestern)
Wednesday 13 April 2011, 16:3017:30
Mon, 18 Apr 2011 11:00:35 +0100
Zaslow, E
Steve Greenham
Isaac Newton Institute
Zaslow, E
539f61a412b98d573298de7430bb06ea
ebed1a5f0e000c2a35f202987b6e83fa
997c93dfb39b386580dbc5a68acf54d7
Zaslow, E (Northwestern)
Wednesday 13 April 2011, 16:3017:30
Zaslow, E (Northwestern)
Wednesday 13 April 2011, 16:3017:30
Cambridge University
3764
http://sms.cam.ac.uk/media/1132205
Ribbon Graphs and Mirror Symmetry
Zaslow, E (Northwestern)
Wednesday 13 April 2011, 16:3017:30
Beginning with a ribbon graph with some extra structure, I will define a dg category, the "constructible plumbing model," which serves as a standin for the Fukaya category of the Riemann surface associated to the ribbon graph. When the graph has a combinatorial version of a torus fibration with section, I will define a onedimensional algebraic curve, and prove that the dg category of vector bundles on the curve is equivalent to the constructible plumbing model, a version of homological mirror symmetry in onedimension. I will also discuss the higherdimensional case.
This talk is based on joint work with Nicolo' Sibilla and David Treumann.
20110418T11:00:42+01:00
3764
1132205
true
16x9
false
no

RingelHall algebras and applications to moduli  I
ucs_sms_1087487_1091280
http://sms.cam.ac.uk/media/1091280
RingelHall algebras and applications to moduli  I
Reineke, M (Bergische Universität Wuppertal)
Wednesday 12 January 2011, 11:3012:30
Fri, 14 Jan 2011 09:20:06 +0000
Reineke, M
Tim Cooper
Isaac Newton Institute
Reineke, M
88e765a76432b9e94d37560cff85253c
7a2ec10b2a8d3020f31234fe9b43dd8d
9ba559bc2c4b3df3dbed846270824bfe
25b924edde98c5a9142ee91f821cd76f
8c7d1d1d0fd84c2cf3cea11f61de7892
Reineke, M (Bergische Universität Wuppertal)
Wednesday 12 January 2011,...
Reineke, M (Bergische Universität Wuppertal)
Wednesday 12 January 2011, 11:3012:30
Cambridge University
3783
http://sms.cam.ac.uk/media/1091280
RingelHall algebras and applications to moduli  I
Reineke, M (Bergische Universität Wuppertal)
Wednesday 12 January 2011, 11:3012:30
Moduli spaces of representations of quivers, parametrizing configurations of vector spaces and linear maps up to base change, provide a prototype for many moduli spaces of algebraic geometry.
The Hall algebra of a quiver, a convolution algebra of functions on stacks of its representations, can be used to obtain quantitative information on the moduli spaces: algebraic identities in the Hall algebra, proved by representationtheoretic techniques, yield identities for e.g. Betti numbers or numbers of points over finite fields.
We will develop several such identities and discuss more recent applications to wallcrossing formulae.
Notes: Several of the Hall algebra techniques which I would like to discuss are reviewed in the survey "Moduli of representations of quivers", arXiv:0802.2147. Although this paper was written for an audience of representation theorists, it might as well be helpful for the participants of the School on Moduli Spaces. The more recent applications to wallcrossing formulae are developed in "Poisson automorphisms and quiver moduli", arXiv:0802.2147.
20110114T09:20:11+00:00
3783
1091280
true
4x3
false
no

RingelHall algebras and applications to moduli  III
ucs_sms_1087487_1091416
http://sms.cam.ac.uk/media/1091416
RingelHall algebras and applications to moduli  III
Reineke, M (Bergische Universität Wuppertal)
Friday 14 January 2011, 11:3012:30
Fri, 14 Jan 2011 19:22:03 +0000
Reineke, M
Tim Cooper
Isaac Newton Institute
Reineke, M
776b5a318f5eb11f11d3b11f3d6b3d66
3eafcdbb1e8cc114ce889f7990f241ba
a1d4beea90687d6c1f990b00b7818d61
053925a63ff557f1fba7444aa5ce5a69
69474d260a868ac1ebffadab115bd52a
Reineke, M (Bergische Universität Wuppertal)
Friday 14 January 2011,...
Reineke, M (Bergische Universität Wuppertal)
Friday 14 January 2011, 11:3012:30
Cambridge University
3500
http://sms.cam.ac.uk/media/1091416
RingelHall algebras and applications to moduli  III
Reineke, M (Bergische Universität Wuppertal)
Friday 14 January 2011, 11:3012:30
Moduli spaces of representations of quivers, parametrizing configurations of vector spaces and linear maps up to base change, provide a prototype for many moduli spaces of algebraic geometry.
The Hall algebra of a quiver, a convolution algebra of functions on stacks of its representations, can be used to obtain quantitative information on the moduli spaces: algebraic identities in the Hall algebra, proved by representationtheoretic techniques, yield identities for e.g. Betti numbers or numbers of points over finite fields.
We will develop several such identities and discuss more recent applications to wallcrossing formulae.
Notes: Several of the Hall algebra techniques which I would like to discuss are reviewed in the survey "Moduli of representations of quivers", arXiv:0802.2147. Although this paper was written for an audience of representation theorists, it might as well be helpful for the participants of the School on Moduli Spaces. The more recent applications to wallcrossing formulae are developed in "Poisson automorphisms and quiver moduli", arXiv:0802.2147.
20110114T19:22:08+00:00
3500
1091416
true
4x3
false
no

Sduality and mirror symmetry in ChernSimons theory
ucs_sms_1087487_1132221
http://sms.cam.ac.uk/media/1132221
Sduality and mirror symmetry in ChernSimons theory
Dimofte, T (Princeton)
Thursday 14 April 2011, 10:0011:00
Mon, 18 Apr 2011 11:19:31 +0100
Dimofte, T
Steve Greenham
Isaac Newton Institute
Dimofte, T
70f267799324465ff3eade76634d4acd
140ab4036a7c41f517339bf55ba672ea
020d2510a538b1629c673056de9fb582
Dimofte, T (Princeton)
Thursday 14 April 2011, 10:0011:00
Dimofte, T (Princeton)
Thursday 14 April 2011, 10:0011:00
Cambridge University
3929
http://sms.cam.ac.uk/media/1132221
Sduality and mirror symmetry in ChernSimons theory
Dimofte, T (Princeton)
Thursday 14 April 2011, 10:0011:00
I will present joint work with S. Gukov on Sduality in threedimensional ChernSimons theories. Upon analytic continuation, the ChernSimons "level" k can be taken to be an arbitrary complex number. Then, both ChernSimons wavefunctions and certain operators that annihilate them acquire a certain symmetry under the inversion of k (Sduality). In terms of the operators, this can be understood in terms of mirror symmetry acting on branes in a hyperkahler space (a Hitchin moduli space).
20110418T11:19:39+01:00
3929
1132221
true
16x9
false
no

Schematic Harder Narasimhan stratification
ucs_sms_1087487_1102037
http://sms.cam.ac.uk/media/1102037
Schematic Harder Narasimhan stratification
Nitsure, N (Tata Institute of Fundamental Research)
Thursday 17 February 2011, 15:3016:30
Thu, 24 Feb 2011 13:09:22 +0000
Nitsure, N
Steve Greenham
Isaac Newton Institute
Nitsure, N
c453802c4de14de9770f02d504a81463
c4a56df96b781c4260f686e21521db2b
c3f693fb00fa13e4356f15ad7988689e
Nitsure, N (Tata Institute of Fundamental Research)
Thursday 17 February 2011,...
Nitsure, N (Tata Institute of Fundamental Research)
Thursday 17 February 2011, 15:3016:30
Cambridge University
3952
http://sms.cam.ac.uk/media/1102037
Schematic Harder Narasimhan stratification
Nitsure, N (Tata Institute of Fundamental Research)
Thursday 17 February 2011, 15:3016:30
The Harder Narasimhan type (in the sense of Gieseker semistability) of a puredimensional coherent sheaf on a projective scheme is known to vary semicontinuously in a flat family, which gives the wellknown Harder Narasimhan stratification of the parameter scheme of the family, by locally closed subsets. We show that each stratum can be endowed with a natural structure of a locally closed subscheme of the parameter scheme, which enjoys an appropriate universal property. As an application, we deduce that puredimensional coherent sheaves of any given Harder Narasimhan type form an Artin algebraic stack. As another application  jointly with L. BrambilaPaz and O. Mata  we describe moduli schemes for certain rank 2 unstable vector bundles on a smooth projective curve, fixing some numerical data.
20110224T13:09:28+00:00
3952
1102037
true
16x9
false
no

Special determinants in higherrank BrillNoether theory
ucs_sms_1087487_1137315
http://sms.cam.ac.uk/media/1137315
Special determinants in higherrank BrillNoether theory
Osserman, B
Thursday 21 April 2011, 15:3016:30
Fri, 06 May 2011 11:07:50 +0100
Osserman, B
Steve Greenham
Isaac Newton Institute
Osserman, B
ada2d69be2d69ad1bc9581397801a820
57004634e77f30dabe5048c2e609c730
bb32a084c90d0bfccc2fb4c85141bdf6
Osserman, B
Thursday 21 April 2011, 15:3016:30
Osserman, B
Thursday 21 April 2011, 15:3016:30
Cambridge University
4153
http://sms.cam.ac.uk/media/1137315
Special determinants in higherrank BrillNoether theory
Osserman, B
Thursday 21 April 2011, 15:3016:30
We give a brief survey of the role of special determinants in higherrank BrillNoether theory, including the original work of Bertram, Feinberg, and Mukai on smooth curves in the case of canonical determinant, generalizations to other determinants, and work (joint with Montserrat Teixidor i Bigas) on degeneration techniques in this context.
20110506T11:07:58+01:00
4153
1137315
true
16x9
false
no

Spectra and Gaps as cohomological theory
ucs_sms_1087487_1126981
http://sms.cam.ac.uk/media/1126981
Spectra and Gaps as cohomological theory
Katzarkov, L
Friday 08 April 2011, 11:3012:30
Mon, 11 Apr 2011 17:57:54 +0100
Katzarkov, L
Steve Greenham
Isaac Newton Institute
Katzarkov, L
15f24a7f7ea5c7df8757bca5c30fd2f9
00ca87d6a9691c43efdd6ad8f893217c
e9bcf325524dfa66c7b060eee4189b05
Katzarkov, L
Friday 08 April 2011, 11:3012:30
Katzarkov, L
Friday 08 April 2011, 11:3012:30
Cambridge University
4006
http://sms.cam.ac.uk/media/1126981
Spectra and Gaps as cohomological theory
Katzarkov, L
Friday 08 April 2011, 11:3012:30
In this lecture we will introduce the theory of spectra and gaps of a category. We will make a connection with theory of algebraic cycles and other classical questions in algebraic geometry.
20110411T17:58:01+01:00
4006
1126981
true
16x9
false
no

Stability and its ramifications
ucs_sms_1087487_1150133
http://sms.cam.ac.uk/media/1150133
Stability and its ramifications
Narasimhan, MS (Tata Institute & Indian Institute of Science)
Monday 13 June 2011, 17:0018:00
Tue, 21 Jun 2011 08:05:28 +0100
Narasimhan, MS
Steve Greenham
Isaac Newton Institute
Narasimhan, MS
042a27f02fafdafa0cc05e42ea821161
95f16ace11de209b31d29274cf59acd5
8a3e9579775d71e61194d7a65c35ae29
Narasimhan, MS (Tata Institute & Indian Institute of Science)
Monday 13 June...
Narasimhan, MS (Tata Institute & Indian Institute of Science)
Monday 13 June 2011, 17:0018:00
Cambridge University
3506
http://sms.cam.ac.uk/media/1150133
Stability and its ramifications
Narasimhan, MS (Tata Institute & Indian Institute of Science)
Monday 13 June 2011, 17:0018:00
The lecture will be concerned with the interaction between algebraic geometry and other major fields of mathematics and physics.The main theme will be the notion of "stability" which arose in moduli problems in algebraic geometry and its relationship with topics in partial differential equations,number theory and physics.
20110621T08:05:37+01:00
3506
1150133
true
16x9
false
no

Stability conditions for the local projective plane
ucs_sms_1087487_1154845
http://sms.cam.ac.uk/media/1154845
Stability conditions for the local projective plane
Bayer, A (Connecticut)
Thursday 30 June 2011, 11:3012:30
Fri, 01 Jul 2011 15:53:06 +0100
Bayer, A
Steve Greenham
Isaac Newton Institute
Bayer, A
c8d5aca079dd3faea3ad11eec943af0d
29bae2adf44c0d023c4f96e927054b8e
c0db0cc62cfd076393399dfa21095ffa
Bayer, A (Connecticut)
Thursday 30 June 2011, 11:3012:30
Bayer, A (Connecticut)
Thursday 30 June 2011, 11:3012:30
Cambridge University
3126
http://sms.cam.ac.uk/media/1154845
Stability conditions for the local projective plane
Bayer, A (Connecticut)
Thursday 30 June 2011, 11:3012:30
Describing the space of Bridgeland stability conditions for the local projective plane turns out to be intimately related to classical results by Drezet and Le Potier on inequalities for Chern classes of slopestable vector bundles on P2. I will describe how this allows one to relate the geometry of this space, and the group of autoequivalences, to the congruence subgroup Gamma1(3). I will also explain a mirror symmetry statement involving the moduli space of elliptic curves with Gamma1(3)level structure. Time permitting, I will also discuss observations on the same problem for local del Pezzo surfaces. This is based on joint work with Emanuele Macrì.
20110701T15:53:15+01:00
3126
1154845
true
16x9
false
no

Stable bundles and holonomy groups of smooth projective varieties
ucs_sms_1087487_1102118
http://sms.cam.ac.uk/media/1102118
Stable bundles and holonomy groups of smooth projective varieties
Balaji, V
Tuesday 22 February 2011, 11:3012:30
Thu, 24 Feb 2011 14:02:45 +0000
Balaji, V
Steve Greenham
Isaac Newton Institute
Balaji, V
8e12fec263f5c2253d382e2b1453f122
99dba7e380bd758f52aa3e36fca0ba39
e5f875b23becad599e5a36c90a11fd49
Balaji, V
Tuesday 22 February 2011, 11:3012:30
Balaji, V
Tuesday 22 February 2011, 11:3012:30
Cambridge University
3835
http://sms.cam.ac.uk/media/1102118
Stable bundles and holonomy groups of smooth projective varieties
Balaji, V
Tuesday 22 February 2011, 11:3012:30
20110224T14:02:51+00:00
3835
1102118
true
16x9
false
no

Stable pairs on local K3 surfaces
ucs_sms_1087487_1131670
http://sms.cam.ac.uk/media/1131670
Stable pairs on local K3 surfaces
Toda, Y (Tokyo)
Tuesday 12 April 2011, 10:0011:00
Fri, 15 Apr 2011 14:18:37 +0100
Toda, Y
Steve Greenham
Isaac Newton Institute
Toda, Y
a3c96e39c771f714a1455882ebbc2c90
c4617b57d83eb5ed6fd46c2150830111
63ee61c67d1b2f2dfb6e77a0da15aef8
Toda, Y (Tokyo)
Tuesday 12 April 2011, 10:0011:00
Toda, Y (Tokyo)
Tuesday 12 April 2011, 10:0011:00
Cambridge University
3728
http://sms.cam.ac.uk/media/1131670
Stable pairs on local K3 surfaces
Toda, Y (Tokyo)
Tuesday 12 April 2011, 10:0011:00
I give a formula which relates Euler characteristic of moduli spaces of stable pairs on local K3 surfaces to counting invariants of semistable sheaves on them. The formula generalizes KawaiYoshioka's formula for stable pairs with irreducible curve classes to arbitrary curve classes. I also propose a conjectual multicovering formula of sheaf counting invariants which, combined with the main result, leads to an Euler characteristic version of KatzKlemmVafa conjecture for stable pairs.
20110415T14:18:44+01:00
3728
1131670
true
16x9
false
no

Stable Schottky relations
ucs_sms_1087487_1147775
http://sms.cam.ac.uk/media/1147775
Stable Schottky relations
ShepherdBarron, N (DPMMS)
Thursday 02 June 2011, 15:3016:30
Fri, 03 Jun 2011 17:08:22 +0100
ShepherdBarron, N
Steve Greenham
Isaac Newton Institute
ShepherdBarron, N
d4a00851120b03495adaede5f88820ab
6c65db4a9210a01a4a382fe9cb8f0bf2
f1b3a16d118a3119673ab7ba9d9bbe24
ShepherdBarron, N (DPMMS)
Thursday 02 June 2011, 15:3016:30
ShepherdBarron, N (DPMMS)
Thursday 02 June 2011, 15:3016:30
Cambridge University
3667
http://sms.cam.ac.uk/media/1147775
Stable Schottky relations
ShepherdBarron, N (DPMMS)
Thursday 02 June 2011, 15:3016:30
The Schottky problem is to find ways of distinguishing Jacobians from arbitrary principally polarized abelian varieties. From a classical viewpoint (that of this talk) the aim is to find Siegel modular forms that vanish along the Jacobian locus. In this talk we discuss what happens in the stable situation, that is, when the genus increases arbitrarily.
20110603T17:08:29+01:00
3667
1147775
true
16x9
false
no

Stable spectral bundles on K3 fibered 3folds
ucs_sms_1087487_1093888
http://sms.cam.ac.uk/media/1093888
Stable spectral bundles on K3 fibered 3folds
Sanchez Gomez, D (Salamanca)
Thursday 20 January 2011, 14:0015:00
Thu, 27 Jan 2011 12:56:18 +0000
Sanchez Gomez, D
Steve Greenham
Isaac Newton Institute
Sanchez Gomez, D
f5f186f8ba2a82fcf5796e9fd44c0bcb
dd5b9f799e0f987429926ce6ff2fa29a
e56ff4d4a1c85395fa33857a180463ea
Sanchez Gomez, D (Salamanca)
Thursday 20 January 2011, 14:0015:00
Sanchez Gomez, D (Salamanca)
Thursday 20 January 2011, 14:0015:00
Cambridge University
3882
http://sms.cam.ac.uk/media/1093888
Stable spectral bundles on K3 fibered 3folds
Sanchez Gomez, D (Salamanca)
Thursday 20 January 2011, 14:0015:00
In this talk I will explain how to construct stable sheaves over K3 fibered threefolds using a relative FourierMukai transform, which describes these sheaves in terms of spectral data. This procedure is similar to the spectral cover construction for elliptic fibrations, which I will also review.
On K3 fibered CalabiYau threefolds, the FourierMukai transform induces an embedding of the relative Jacobian of line bundles on spectral covers into the moduli space of sheaves of given invariants. This makes the moduli space of spectral sheaves to a generic torus fibration over the moduli space of curves of given arithmetic genus on the CalabiYau threefold.
20110127T12:56:23+00:00
3882
1093888
true
16x9
false
no

The L2 geometry of vortex moduli spaces
ucs_sms_1087487_1105231
http://sms.cam.ac.uk/media/1105231
The L2 geometry of vortex moduli spaces
Speight, M (Leeds)
Thursday 24 February 2011, 15:3016:30
Fri, 04 Mar 2011 10:30:12 +0000
Speight, M
Steve Greenham
Isaac Newton Institute
Speight, M
0cb05bd3999269aa8c215555eb85ee1e
4e17f60635c90528efd394286acd6134
9eb5a5d4863d6e740c493478bd4f477f
Speight, M (Leeds)
Thursday 24 February 2011, 15:3016:30
Speight, M (Leeds)
Thursday 24 February 2011, 15:3016:30
Cambridge University
4227
http://sms.cam.ac.uk/media/1105231
The L2 geometry of vortex moduli spaces
Speight, M (Leeds)
Thursday 24 February 2011, 15:3016:30
Let L be a hermitian line bundle over a Riemann surface X. A vortex is a pair consisting of a section of and a connexion on L satisfying a certain pair of coupled differential equations similar to the Hitchin equations. The moduli space of vortices is topologically rather simple. The interesting point is that it has a canonical kaehler structure, geodesics of which are conjectured to approximate the low energy dynamics of vortices. In this talk I will review what is known about this kaehler geometry, focussing mainly on the cases where X is the plane, sphere or hyperbolic plane.
20110304T10:30:17+00:00
4227
1105231
true
16x9
false
no

The locus of intermediate Jabobians of cubic threefolds
ucs_sms_1087487_1097704
http://sms.cam.ac.uk/media/1097704
The locus of intermediate Jabobians of cubic threefolds
Hulek, K (University of Hannover)
Thursday 10 February 2011, 14:0015:00
Mon, 14 Feb 2011 15:18:09 +0000
Hulek, K
Steve Greenham
Isaac Newton Institute
Hulek, K
322e6cc84a482038af5c2646d86f1db9
070eb2ab34362e4ef348865639ed86f4
396cc486b623b10eeef8fa43c795e5f4
Hulek, K (University of Hannover)
Thursday 10 February 2011, 14:0015:00
Hulek, K (University of Hannover)
Thursday 10 February 2011, 14:0015:00
Cambridge University
3685
http://sms.cam.ac.uk/media/1097704
The locus of intermediate Jabobians of cubic threefolds
Hulek, K (University of Hannover)
Thursday 10 February 2011, 14:0015:00
We study the (closure of the) locus of intermediate Jacobians of cubic threefolds in the perfect cone compactification of the moduli space of principally polarized abelian fivefolds for which we obtain an expression in the tautological Chow ring. We also discuss possible generalizations of this locus in higher dimensions. This is joint work with S. Grushevsky.
20110214T15:18:15+00:00
3685
1097704
true
16x9
false
no

The motivic DonaldsonThomas invariants of fat points
ucs_sms_1087487_1126658
http://sms.cam.ac.uk/media/1126658
The motivic DonaldsonThomas invariants of fat points
Davison , B (Oxford)
Wednesday 06 April 2011, 16:3017:30
Mon, 11 Apr 2011 14:20:51 +0100
Davison , B
Steve Greenham
Isaac Newton Institute
Davison , B
3f606c1e03c7064a01d3a5006eb67f69
a8266bd11d7df03e0899dfcc78ac9b52
9dcefcf81ecee86e0c13e9bc5f6d2d6d
Davison , B (Oxford)
Wednesday 06 April 2011, 16:3017:30
Davison , B (Oxford)
Wednesday 06 April 2011, 16:3017:30
Cambridge University
3531
http://sms.cam.ac.uk/media/1126658
The motivic DonaldsonThomas invariants of fat points
Davison , B (Oxford)
Wednesday 06 April 2011, 16:3017:30
Recent work of Behrend, Bryan and Szendroi gives a nice handle on the degree zero motivic DonaldsonThomas invariants of threefolds, in which the calculation of the invariants of a single point in smooth three dimensional space plays the key role. I will explain how fat points fit naturally into the theory of 3CalabiYau categories, and also what kind of contributions they make. In contrast with the smooth case, the story here throws up complicated motives and monodromy actions, and it is possible to see directly here the role played by the concept of orientation data.
20110411T14:20:59+01:00
3531
1126658
true
16x9
false
no

The PfaffianGrassmannian correspondence via LandauGinzburg models
ucs_sms_1087487_1126639
http://sms.cam.ac.uk/media/1126639
The PfaffianGrassmannian correspondence via LandauGinzburg models
Segal, E
Wednesday 06 April 2011, 11:3012:30
Mon, 11 Apr 2011 14:04:54 +0100
Segal, E
Steve Greenham
Isaac Newton Institute
Segal, E
b7f2347be478445a2e41aaef98c03f8f
f7114b025fe95d43e29fb63252b0c18f
2ecc1aac3db37195a2232354ec9d555a
Segal, E
Wednesday 06 April 2011, 11:3012:30
Segal, E
Wednesday 06 April 2011, 11:3012:30
Cambridge University
3206
http://sms.cam.ac.uk/media/1126639
The PfaffianGrassmannian correspondence via LandauGinzburg models
Segal, E
Wednesday 06 April 2011, 11:3012:30
The PfaffianGrassmannian correspondence is an example of a derived equivalence between two CalabiYau threefolds that are not birational. Hori and Tong have given a physical explanation of the correspondence, I'll describe some workinprogress that is trying to interpret their work mathematically, using categories of Bbranes in LandauGinzburg models.
20110411T14:05:00+01:00
3206
1126639
true
16x9
false
no

The polynomial method in combinatorial incidence geometry
ucs_sms_1087487_1102020
http://sms.cam.ac.uk/media/1102020
The polynomial method in combinatorial incidence geometry
Tao, T (University of California, Los Angeles)
Thursday 17 February 2011, 14:0015:00
Thu, 24 Feb 2011 12:59:55 +0000
Tao, T
Steve Greenham
Isaac Newton Institute
Tao, T
93e3a599974e8da845783b399dac86f0
0594bf4a2e0a17216bda5f754ab037ac
589cd6b6b2a498166c139f25cdf28999
Tao, T (University of California, Los Angeles)
Thursday 17 February 2011,...
Tao, T (University of California, Los Angeles)
Thursday 17 February 2011, 14:0015:00
Cambridge University
3608
http://sms.cam.ac.uk/media/1102020
The polynomial method in combinatorial incidence geometry
Tao, T (University of California, Los Angeles)
Thursday 17 February 2011, 14:0015:00
Combinatorial incidence geometry is concerned with controlling the number of possible incidences between a finite number of geometric objects such as points, lines, and circles, in various domains. Recently, a number of breakthroughs in the subject (such as Dvir's solution of the finite field Kakeya conjecture, or Guth and Katz's nearcomplete solution of the Erdos distance problem) have been obtained by applying the _polynomial method_, in which one uses linear algebra (or algebraic topology) to efficiently captures many of these objects inside an algebraic variety of controlled degree, and then uses tools from algebraic geometry to understand how this variety interacts with the other objects being studied. In this talk we give an introduction to these methods.
20110224T13:00:00+00:00
3608
1102020
true
16x9
false
no

The stable pairs theory of local curves with stationary descendents
ucs_sms_1087487_1126618
http://sms.cam.ac.uk/media/1126618
The stable pairs theory of local curves with stationary descendents
Pixton, A
Tuesday 05 April 2011, 16:3017:30
Mon, 11 Apr 2011 13:52:09 +0100
Pixton, A
Steve Greenham
Isaac Newton Institute
Pixton, A
c4fc18ab267eb85570851dd8a39653e4
52da1ba7467fb5aae0074e3b7caf5017
e4934d4233925c67da7224e736309190
Pixton, A
Tuesday 05 April 2011, 16:3017:30
Pixton, A
Tuesday 05 April 2011, 16:3017:30
Cambridge University
3432
http://sms.cam.ac.uk/media/1126618
The stable pairs theory of local curves with stationary descendents
Pixton, A
Tuesday 05 April 2011, 16:3017:30
The counting function associated to the moduli space of stable pairs on a 3fold is conjectured to give the Laurent expansion of a rational function. I will discuss a simple proof of this conjecture in the local curve case with only stationary descendent insertions. The proof uses a combination of reduction rules for descendents and some exact calculations involving the stable pairs vertex. This talk presents joint work with Rahul Pandharipande.
20110411T13:52:15+01:00
3432
1126618
true
16x9
false
no

Topology of moduli spaces of vector bundles on a real algebraic curve
ucs_sms_1087487_1154538
http://sms.cam.ac.uk/media/1154538
Topology of moduli spaces of vector bundles on a real algebraic curve
Schaffhauser, FMR (Los Andes)
Tuesday 28 June 2011, 14:4015:10
Thu, 30 Jun 2011 09:02:39 +0100
Schaffhauser, FMR
Steve Greenham
Isaac Newton Institute
Schaffhauser, FMR
90c0be623f57433de2a1ce4f6193f178
823b8bb66ded86ba2dba204c21c8eed2
d68e61380bb2816947e794e15f644163
Schaffhauser, FMR (Los Andes)
Tuesday 28 June 2011, 14:4015:10
Schaffhauser, FMR (Los Andes)
Tuesday 28 June 2011, 14:4015:10
Cambridge University
1879
http://sms.cam.ac.uk/media/1154538
Topology of moduli spaces of vector bundles on a real algebraic curve
Schaffhauser, FMR (Los Andes)
Tuesday 28 June 2011, 14:4015:10
Moduli spaces of real and quaternionic vector bundles on a curve can be expressed as Lagrangian quotients and embedded into the symplectic quotient corresponding to the moduli variety of holomorphic vector bundles of fixed rank and degree on a smooth complex projective curve. From the algebraic point of view, these Lagrangian quotients are irreducible sets of real points inside a complex moduli variety endowed with an antiholomorphic involution. This presentation as a quotient enables us to generalise the equivariant methods of Atiyah and Bott to a setting with involutions, and compute the mod 2 Poincaré series of these real algebraic varieties. This is joint work with ChiuChu Melissa Liu (Columbia).
20110630T09:02:50+01:00
1879
1154538
true
16x9
false
no

Towards a geometric compactification of moduli of polarized K3 surfaces
ucs_sms_1087487_1149158
http://sms.cam.ac.uk/media/1149158
Towards a geometric compactification of moduli of polarized K3 surfaces
Keel, S (Texas)
Tuesday 07 June 2011, 10:0011:00
Mon, 13 Jun 2011 10:41:04 +0100
Keel, S
Steve Greenham
Isaac Newton Institute
Keel, S
c7ebaab6fa01a4d186d20fd51b2d43ac
ea7588e7f9f34008ff1d6fbcc3dcf121
d7140037ccb4b3916ec663bf587dd935
Keel, S (Texas)
Tuesday 07 June 2011, 10:0011:00
Keel, S (Texas)
Tuesday 07 June 2011, 10:0011:00
Cambridge University
4484
http://sms.cam.ac.uk/media/1149158
Towards a geometric compactification of moduli of polarized K3 surfaces
Keel, S (Texas)
Tuesday 07 June 2011, 10:0011:00
I'll discuss my recent proof, joint with Hacking and Gross, of Tyurin's conjecture on canonical theta functions for polarized K3 surface, and our expectation that the construction determines a canonical toroidal compactification of moduli of polarized K3 surfaces, such that the universal family extends to a family of SLC Gorenstein Ktrivial surfaces.
20110613T10:41:13+01:00
4484
1149158
true
16x9
false
no

Trivertices and a corresponding class of hyperKahler spaces
ucs_sms_1087487_1131634
http://sms.cam.ac.uk/media/1131634
Trivertices and a corresponding class of hyperKahler spaces
Hanany, A (Imperial College London)
Monday 11 April 2011, 16:3017:30
Fri, 15 Apr 2011 13:16:53 +0100
Hanany, A
Steve Greenham
Isaac Newton Institute
Hanany, A
efaf2d064a8386cf1f7797f8445c5fbc
c6599590b72448bfa20e3c6833d30bea
cdc95b4e23a3fd3da4e8fb6e63e83ffd
Hanany, A (Imperial College London)
Monday 11 April 2011, 16:3017:30
Hanany, A (Imperial College London)
Monday 11 April 2011, 16:3017:30
Cambridge University
4115
http://sms.cam.ac.uk/media/1131634
Trivertices and a corresponding class of hyperKahler spaces
Hanany, A (Imperial College London)
Monday 11 April 2011, 16:3017:30
Given a graph with lines and 3valent vertices, one can construct, using a simple dictionary, a Lagrangian that has N=2 supersymmetry in 3+1 dimensions. The vacuum moduli space of such a theory is well known to give moment map equations for a HyperKahler manifold.
We will discuss the class of hyperkahler manifolds which arise due to such a construction and present their special properties. The Hilbert Series of these spaces can be computed and turns out to be a function of the number of external legs and loops in the graph but not on its detailed structure. The corresponding SCFT consequence of this property indicates a crucial universality of many Lagrangians, all of which have the same dynamics.
The talk is based on http://arXiv.org/pdf/1012.2119
20110415T13:17:01+01:00
4115
1131634
true
16x9
false
no

UhlenbeckDonaldson compactification for framed sheaves
ucs_sms_1087487_1147758
http://sms.cam.ac.uk/media/1147758
UhlenbeckDonaldson compactification for framed sheaves
Bruzzo, U (SISSA)
Thursday 02 June 2011, 14:0015:00
Fri, 03 Jun 2011 16:48:02 +0100
Bruzzo, U
Steve Greenham
Isaac Newton Institute
Bruzzo, U
6cf38117bc29c9a89341a25a062bb417
d166868cb94846d9bf7149edc689562b
843de39ae6f3fb61734e680dbacfb613
Bruzzo, U (SISSA)
Thursday 02 June 2011, 14:0015:00
Bruzzo, U (SISSA)
Thursday 02 June 2011, 14:0015:00
Cambridge University
3442
http://sms.cam.ac.uk/media/1147758
UhlenbeckDonaldson compactification for framed sheaves
Bruzzo, U (SISSA)
Thursday 02 June 2011, 14:0015:00
We study moduli spaces of framed sheaves on projective surfaces and introduce a "partial compactification" a la UhlenbeckDonaldson for them.
20110603T16:48:10+01:00
3442
1147758
true
16x9
false
no

Universal plane curve and moduli spaces of 1dimensional coherent sheaves
ucs_sms_1087487_1154556
http://sms.cam.ac.uk/media/1154556
Universal plane curve and moduli spaces of 1dimensional coherent sheaves
Iena, O (SISSA)
Tuesday 28 June 2011, 15:2015:50
Thu, 30 Jun 2011 09:09:14 +0100
Iena, O
Steve Greenham
Isaac Newton Institute
Iena, O
9a68cd608cd75e41e090141660d1f706
25d833c7b7326f7fd59bcce45457fee9
579f562bcd222d783dfd39a34e574e5d
Iena, O (SISSA)
Tuesday 28 June 2011, 15:2015:50
Iena, O (SISSA)
Tuesday 28 June 2011, 15:2015:50
Cambridge University
1583
http://sms.cam.ac.uk/media/1154556
Universal plane curve and moduli spaces of 1dimensional coherent sheaves
Iena, O (SISSA)
Tuesday 28 June 2011, 15:2015:50
We show that the universal plane curve M of degree d may be seen as a space of isomorphism classes of certain 1dimensional coherent sheaves on the projective plane. The universal singular locus M' of M coincides with the subvariety of M consisting of sheaves that are not locally free on their support. It turns out that the blow up of M along M' may be naturally seen as a compactification of M_B=M\M' by vector bundles (on support).
20110630T09:09:23+01:00
1583
1154556
true
16x9
false
no

Vector bundles and coherent systems on nodal curves
ucs_sms_1087487_1149200
http://sms.cam.ac.uk/media/1149200
Vector bundles and coherent systems on nodal curves
Bhosle, U (TIFR)
Thursday 09 June 2011, 14:0015:00
Mon, 25 Jul 2011 10:17:30 +0100
Bhosle, U
Steve Greenham
Isaac Newton Institute
Bhosle, U
61ca47501462545091772346f0db60ff
8cddd2f2d227a3bb37a75e02429ae0fb
999929bcd28b09b665d4642c3dc54b94
Bhosle, U (TIFR)
Thursday 09 June 2011, 14:0015:00
Bhosle, U (TIFR)
Thursday 09 June 2011, 14:0015:00
Cambridge University
3148
http://sms.cam.ac.uk/media/1149200
Vector bundles and coherent systems on nodal curves
Bhosle, U (TIFR)
Thursday 09 June 2011, 14:0015:00
We study moduli spaces of coherent systems on an irreducible rational curve with one node. We determine the conditions for emptiness and nonemptiness of these moduli spaces. We study the properties like irreducibility, smoothness, seminormality and rationality of the moduli spaces.
20110725T10:17:39+01:00
3148
1149200
true
16x9
false
no

Vector bundles on the algebraic 5sphere and punctured affine 3space
ucs_sms_1087487_1147616
http://sms.cam.ac.uk/media/1147616
Vector bundles on the algebraic 5sphere and punctured affine 3space
Yu, J (ETH Zurich)
Tuesday 24 May 2011, 11:3012:30
Fri, 03 Jun 2011 15:01:33 +0100
Yu, J
Steve Greenham
Isaac Newton Institute
Yu, J
66c4cc9a5d68ea90ada89d920d69fa82
ae2781437aa1f586ea9496e18abf4b15
340b07019a80fa77d9d1f075a7a0b000
Yu, J (ETH Zurich)
Tuesday 24 May 2011, 11:3012:30
Yu, J (ETH Zurich)
Tuesday 24 May 2011, 11:3012:30
Cambridge University
3280
http://sms.cam.ac.uk/media/1147616
Vector bundles on the algebraic 5sphere and punctured affine 3space
Yu, J (ETH Zurich)
Tuesday 24 May 2011, 11:3012:30
The 5dimensional complex sphere X is isomorphic to SL_3/S_2, which admits a fibration p: X>Y to the 3dimensional punctured affine space Y=C^{3}\{0} with C^{2} fibres. It was shown by Fabien Morel that vector bundles on a smooth affine variety are determined by A^{1}homotopy classes of maps to BGL. The fibration p is an A^{1}homotopy weak equivalence but the Y above is not affine, so it is natural to look for nonisomorphic vector bundles on Y with isomorphic pullbacks to X. We give interesting examples of such bundles of any rank bigger than 1. The examples are produced from vector bundles on the projective space P=P^2.
20110603T15:01:41+01:00
3280
1147616
true
16x9
false
no

Virtual classes, Quot schemes and stable quotients
ucs_sms_1087487_1150197
http://sms.cam.ac.uk/media/1150197
Virtual classes, Quot schemes and stable quotients
Oprea, D (UCSD)
Thursday 16 June 2011, 14:0015:00
Tue, 21 Jun 2011 10:47:35 +0100
Oprea, D
Steve Greenham
Isaac Newton Institute
Oprea, D
bf874b8313f4da83a51c3ea47e797b7c
361c8c01d0476dd4fd06a551c08f1ac5
df5d7c8c66005fb274943feb0a311c1f
Oprea, D (UCSD)
Thursday 16 June 2011, 14:0015:00
Oprea, D (UCSD)
Thursday 16 June 2011, 14:0015:00
Cambridge University
3727
http://sms.cam.ac.uk/media/1150197
Virtual classes, Quot schemes and stable quotients
Oprea, D (UCSD)
Thursday 16 June 2011, 14:0015:00
The theme of the talk is the construction of virtual fundamental classes for a Quot schemes of curves. First, I will explain the construction for smooth projective curves. Then, letting the curve vary in moduli, we obtain the space of stable quotients. Over nodal curves, a modification of the Quot scheme is necessary: a relative construction is made to keep the torsion of the quotient away from singularities. The resulting space can be used to study the GromovWitten theory of Grassmannians.
20110621T10:47:45+01:00
3727
1150197
true
16x9
false
no

Vortices on Riemann Surfaces
ucs_sms_1087487_1154594
http://sms.cam.ac.uk/media/1154594
Vortices on Riemann Surfaces
Manton, N (Cambridge)
Wednesday 29 June 2011, 10:0011:00
Thu, 30 Jun 2011 09:43:14 +0100
Manton, N
Steve Greenham
Isaac Newton Institute
Manton, N
8b38755fc76cdb66ec7bb3bcff591f45
34a1defc4d5e05805bd763beb7282ce4
8ca24d01c986f330ca04cbe71cf41559
Manton, N (Cambridge)
Wednesday 29 June 2011, 10:0011:00
Manton, N (Cambridge)
Wednesday 29 June 2011, 10:0011:00
Cambridge University
3908
http://sms.cam.ac.uk/media/1154594
Vortices on Riemann Surfaces
Manton, N (Cambridge)
Wednesday 29 June 2011, 10:0011:00
We will discuss the geometry and physics of U(1) vortex solutions on compact Riemann surfaces. The moduli space of Nvortex solutions has a natural Riemannian metric, for which there is a localised expression (SamolsStrachan) although this is not known explicitly. The volume of the moduli space is known, leading to an equation of state for a vortex gas. An asymptotic expression for the moduli space metric for one vortex on a large surface has been obtained, which could be developed further (Dunajski & Manton). The metric is also understood in the limit of a small surface, where the vortex dissolves (Manton & Romao).
20110630T09:43:23+01:00
3908
1154594
true
16x9
false
no

Why descendents?
ucs_sms_1087487_1131719
http://sms.cam.ac.uk/media/1131719
Why descendents?
Pandharipande, R (Princeton)
Tuesday 12 April 2011, 11:3012:30
Fri, 15 Apr 2011 14:35:26 +0100
Pandharipande, R
Steve Greenham
Isaac Newton Institute
Pandharipande, R
fb8861c64e33b66e4faf51adc3646571
6785f2e134d2c2f2e055d8ee1d323f89
01149bd622a95755788c4e26237631fc
Pandharipande, R (Princeton)
Tuesday 12 April 2011, 11:3012:30
Pandharipande, R (Princeton)
Tuesday 12 April 2011, 11:3012:30
Cambridge University
3845
http://sms.cam.ac.uk/media/1131719
Why descendents?
Pandharipande, R (Princeton)
Tuesday 12 April 2011, 11:3012:30
I will discuss several motivations and results concerning descendents in 3fold sheaf theories.
20110415T14:35:33+01:00
3845
1131719
true
16x9
false
no
1087487