3
Workshop on Kahler Geometry
http://sms.cam.ac.uk/collection/1243544
Workshop on Kahler Geometry held and the Center for Mathematical Sciences, April 10 to April 13 2012 organized by Julius Ross and Ivan Cheltsov.
Workshop website: http://www.maths.ed.ac.uk/cheltsov/cambridge/index.html
Supported by a Marie Curie Reintegration Grant within the 7th European Community Framework Programme. We wish to acknowledge additional support from Sidney Sussex College and the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge.
Videos filmed by Jesus MartinezGarcia and Dima Sakovich.
1440
2015
Fri, 29 May 2015 16:49:44 +0100
Wed, 18 Apr 2012 09:59:07 +0100
en
smssupport@uis.cam.ac.uk
Workshop on Kahler Geometry
http://sms.cam.ac.uk/collection/1243544
http://rss.sms.cam.ac.uk/itunesimage/1247497.jpg
http://video.search.yahoo.com/mrss
Workshop on Kahler Geometry
Workshop on Kahler Geometry held and the Center for Mathematical Sciences, April 10 to April 13 2012 organized by Julius Ross and Ivan Cheltsov.
Workshop website: http://www.maths.ed.ac.uk/cheltsov/cambridge/index.html
Supported by a Marie Curie Reintegration Grant within the 7th European Community Framework Programme. We wish to acknowledge additional support from Sidney Sussex College and the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge.
Videos filmed by Jesus MartinezGarcia and Dima Sakovich.
Workshop on Kahler Geometry
Workshop on Kahler Geometry held and the Center for Mathematical Sciences, April 10 to April 13 2012 organized by Julius Ross and Ivan Cheltsov.
Workshop website: http://www.maths.ed.ac.uk/cheltsov/cambridge/index.html
Supported by a Marie Curie Reintegration Grant within the 7th European Community Framework Programme. We wish to acknowledge additional support from Sidney Sussex College and the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge.
Videos filmed by Jesus MartinezGarcia and Dima Sakovich.
Cambridge University
Dr J. Ross
J.Ross@dpmms.cam.ac.uk
http://sms.cam.ac.uk/collection/1243544
Workshop on Kahler Geometry
20120418T09:59:07+01:00
DPMMS
100438
no

A BrunnMinkowski theorem for Fano manifolds and some uniqueness theorems in Kahler geometry (Bo Berndtsson)
ucs_sms_1243544_1247313
http://sms.cam.ac.uk/media/1247313
A BrunnMinkowski theorem for Fano manifolds and some uniqueness theorems in Kahler geometry (Bo Berndtsson)
Tue, 24 Apr 2012 08:43:12 +0100
108
108104
Bo Berndtsson
University of Cambridge
Dr J. Ross
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Cambridge University
3486
http://sms.cam.ac.uk/media/1247313
A BrunnMinkowski theorem for Fano manifolds and some uniqueness theorems in Kahler geometry (Bo Berndtsson)
20120424T10:26:47+01:00
3486
1247313
true
16x9
false
no

A probabilistic approach to KahlerEinstein metrics (Robert Berman)
ucs_sms_1243544_1245708
http://sms.cam.ac.uk/media/1245708
A probabilistic approach to KahlerEinstein metrics (Robert Berman)
Slides for this talk available at http://www.maths.ed.ac.uk/cheltsov/cambridge/schedule.html
Sun, 22 Apr 2012 01:17:43 +0100
108
108104
Robert Berman
University of Cambridge
Dr J. Ross
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Slides for this talk available at...
Slides for this talk available at http://www.maths.ed.ac.uk/cheltsov/cambridge/schedule.html
Cambridge University
3505
http://sms.cam.ac.uk/media/1245708
A probabilistic approach to KahlerEinstein metrics (Robert Berman)
Slides for this talk available at http://www.maths.ed.ac.uk/cheltsov/cambridge/schedule.html
20120424T10:45:48+01:00
3505
1245708
true
16x9
false
no

Ambitoric structures and extremal Kahler orbisurfaces with b_2(M)=2 (Vestislav Apostolov)
ucs_sms_1243544_1246710
http://sms.cam.ac.uk/media/1246710
Ambitoric structures and extremal Kahler orbisurfaces with b_2(M)=2 (Vestislav Apostolov)
Mon, 23 Apr 2012 10:26:35 +0100
108
108104
Vestislav Apostolov
University of Cambridge
Dr J. Ross
7c26a9e135d31f31704957cfd3df9320
1bc59e3c61d2d275f4bee6f26dbd3e7b
Cambridge University
3690
http://sms.cam.ac.uk/media/1246710
Ambitoric structures and extremal Kahler orbisurfaces with b_2(M)=2 (Vestislav Apostolov)
I will discuss an explicit resolution of the existence problem for extremal Kahler metrics on toric 4orbifolds $M$ with second Betti number equal to 2.
More precisely, I will show that $M$ admits such a metric if and only if its rational Delzant polytope (which is a labelled quadrilateral) is K polystable in the relative, toric sense (as studied by S. Donaldson, G. Szekelyhidi et al.). Furthermore, in this case, the extremal Kahler metric is ambitoric, i.e., compatible with a conformally equivalent, oppositely oriented toric Kahler metric, which turns out also to be extremal.
Among the explicit extremal Kahler metrics obtained, there are conformally Einstein examples which are Riemannian analogues of the exact solutions of the Einstein equations in General Relativity, found by R. Debever, N. Kamran, and R. McLenaghan. This is a joint work with D. Calderbank and P. Gauduchon.
20120424T13:49:17+01:00
3690
1246710
true
16x9
true
no

Applications of the Hormander technique in KahlerEinstein geometry (Simon Donaldson)
ucs_sms_1243544_1247397
http://sms.cam.ac.uk/media/1247397
Applications of the Hormander technique in KahlerEinstein geometry (Simon Donaldson)
Tue, 24 Apr 2012 09:46:53 +0100
108
108104
Simon Donaldson
University of Cambridge
Dr J. Ross
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Cambridge University
3957
http://sms.cam.ac.uk/media/1247397
Applications of the Hormander technique in KahlerEinstein geometry (Simon Donaldson)
20120424T13:49:57+01:00
3957
1247397
true
16x9
false
no

Bounding singularities on minimal models (Paolo Cascini)
ucs_sms_1243544_1247476
http://sms.cam.ac.uk/media/1247476
Bounding singularities on minimal models (Paolo Cascini)
Fri, 04 May 2012 08:36:11 +0100
108
108104
Paolo Cascini
University of Cambridge
Dr J. Ross
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Cambridge University
3649
http://sms.cam.ac.uk/media/1247476
Bounding singularities on minimal models (Paolo Cascini)
Thanks to Mori’s program, we can associate to any 3dimensional complex projective manifold X, a minimal model, which is a projective variety birational to X and whose canonical class is well behaved. Unfortunately this model is not always unique or smooth. We describe a method to bound the singularities of a minimal model of X depending on its topology.
20120504T08:36:29+01:00
3649
1247476
true
16x9
false
no

Convergence of the normalized KaehlerRicci flow on Fano varieties (Vincent Guedj)
ucs_sms_1243544_1247447
http://sms.cam.ac.uk/media/1247447
Convergence of the normalized KaehlerRicci flow on Fano varieties (Vincent Guedj)
Wed, 09 May 2012 08:53:26 +0100
108
108104
Vincent Guedj
University of Cambridge
Dr J. Ross
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8493dff461b6c6bb4b9d83c0145a1225
Cambridge University
3765
http://sms.cam.ac.uk/media/1247447
Convergence of the normalized KaehlerRicci flow on Fano varieties (Vincent Guedj)
Let X be a Fano manifold whose Mabuchi functional is proper. A deep result of PerelmanTianZhu asserts that the normalized KaehlerRicci flow, starting from an arbitrary Kaehler form in c_1(X), smoothly converges towards the unique KaehlerEinstein metric. We will explain an alternative proof of a weaker convergence result which applies to the broader context of (log)Fano varieties.
20120509T08:53:43+01:00
3765
1247447
true
16x9
false
no

Gluing theorems and power series (Michael Singer)
ucs_sms_1243544_1247418
http://sms.cam.ac.uk/media/1247418
Gluing theorems and power series (Michael Singer)
Tue, 24 Apr 2012 09:56:43 +0100
108
108104
Michael Singer
University of Cambridge
Dr J. Ross
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0cd6793169f10ad5ef115074820a1e47
Cambridge University
3324
http://sms.cam.ac.uk/media/1247418
Gluing theorems and power series (Michael Singer)
20120424T10:35:04+01:00
3324
1247418
true
16x9
false
no

Hprojective geometry: an overview (David Calderbank)
ucs_sms_1243544_1243634
http://sms.cam.ac.uk/media/1243634
Hprojective geometry: an overview (David Calderbank)
Slides for this talk available at http://www.maths.ed.ac.uk/cheltsov/cambridge/schedule.html
Mon, 23 Apr 2012 08:31:47 +0100
mathematics,geometry
108
108104
David Calderbank
University of Cambridge
Dr J. Ross
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Slides for this talk available at...
Slides for this talk available at http://www.maths.ed.ac.uk/cheltsov/cambridge/schedule.html
Cambridge University
3355
mathematics,geometry
http://sms.cam.ac.uk/media/1243634
Hprojective geometry: an overview (David Calderbank)
Slides for this talk available at http://www.maths.ed.ac.uk/cheltsov/cambridge/schedule.html
Hprojective geometry is a complex analogue of projective geometry in which the projective connection is not assumed holomorphic. It interacts with Kahler geometry in numerous ways, which have been studied by different authors, often independently and with different motivations.
The aim of this talk is to introduce the topic and draw some of these threads together, including hamiltonian 2forms, Tanno equations, Hprojective equivalence, holonomy of Cartan connections, almost Kahler geometry of 4manifolds, and quaternionic geometry of (co)tangent bundles.
20120424T10:47:10+01:00
3355
1243634
true
16x9
true
no

K(pi,1)property of complements to curve arrangements on surfaces (Dmitri Panov)
ucs_sms_1243544_1247684
http://sms.cam.ac.uk/media/1247684
K(pi,1)property of complements to curve arrangements on surfaces (Dmitri Panov)
Tue, 24 Apr 2012 13:47:51 +0100
108
108104
Dmitri Panov
University of Cambridge
Dr J. Ross
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1a549ae05e2e5fa3d183837694fcc444
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Cambridge University
3992
http://sms.cam.ac.uk/media/1247684
K(pi,1)property of complements to curve arrangements on surfaces (Dmitri Panov)
It is a nontrivial question to understand when a complement to a collection of curves on a complex surface is of type K(pi,1). We will explain that such a property (which is rather rare by itself) holds in cases when one can construct on the surface a nonpositively curved Kaehler metric with conical singularities of angles less than 2pi along the collection of curves.
20120424T13:48:05+01:00
3992
1247684
true
16x9
false
no

Lagrangian fibrations on hyperkahler manifolds (Daniel Greb)
ucs_sms_1243544_1247327
http://sms.cam.ac.uk/media/1247327
Lagrangian fibrations on hyperkahler manifolds (Daniel Greb)
Tue, 24 Apr 2012 09:10:02 +0100
108
108104
Daniel Greb
University of Cambridge
Dr J. Ross
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6f0c0e2e6f33d17890e706bcbc69fff1
dcb6e41a138aaf6b00a7b8e083023626
Cambridge University
3085
http://sms.cam.ac.uk/media/1247327
Lagrangian fibrations on hyperkahler manifolds (Daniel Greb)
The general fibre of a Lagrangian fibration on a hyperkahler manifold is a Lagrangian torus. It is a question of Beauville whether any Lagrangian torus in a hyperkahler manifold arises in this way.
In my talk, I will describe recent joint work with Christian Lehn and Sonke Rollenske giving a positive answer to Beauville’s question in the nonprojective case. Furthermore, I will derive a criterion for the existence of a Lagrangian fibration in the projective case, which has recently been used by JunMuk Hwang to provide a positive answer to Beauville’s question for projective hyperkahler manifolds.
20120424T10:33:46+01:00
3085
1247327
true
16x9
false
no

Quantisation and the Hessian of Mabuchi energy (Joel Fine)
ucs_sms_1243544_1247433
http://sms.cam.ac.uk/media/1247433
Quantisation and the Hessian of Mabuchi energy (Joel Fine)
Tue, 24 Apr 2012 10:12:27 +0100
Joel Fine
University of Cambridge
Dr J. Ross
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9adb77078f627c38fc87d074f71a64d0
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Cambridge University
3495
http://sms.cam.ac.uk/media/1247433
Quantisation and the Hessian of Mabuchi energy (Joel Fine)
Let L be an ample line bundle over a compact complex manifold. In Kähler quantisation one approximates the space H of Kähler metrics in c_1(L) by the spaces B_k of Hermitian innerproducts on H0(X,Lk). Following Donaldson, we know that Mabuchi energy E on H is “quantised” by balancing energy F_k, a function on B_k.
I will explain a result in this vein, namely that the Hessian D of E, a 4th order selfadjoint elliptic operator on functions, is quantised by the Hessians P_k of the F_k, operators on the space of Hermitian endomorphisms of H^0 (X,Lk) defined purely in terms of projective embeddings. In particular, the eigenvalues and eigenspaces of P_k converge to those of D. I will explain applications of this result as well as aspects of its proof.
20120424T10:40:56+01:00
3495
1247433
true
16x9
false
no

Sasaki geometry and positive curvature (Song Sun)
ucs_sms_1243544_1247661
http://sms.cam.ac.uk/media/1247661
Sasaki geometry and positive curvature (Song Sun)
Fri, 04 May 2012 09:48:52 +0100
108
108104
Song Sun
University of Cambridge
Dr J. Ross
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1c24f89bca3762f848c9455ccb076f45
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Cambridge University
3679
http://sms.cam.ac.uk/media/1247661
Sasaki geometry and positive curvature (Song Sun)
We classify simply connected compact Sasaki manifolds with positive transverse bisectional curvature. In particular, the moduli space of all such manifolds can be contracted to a point—the standard round sphere. This provides an alternative proof of the MoriSiuYau theorem on Frankel conjecture as well as extends it to the orbifold case.
The proof involves deforming any such manifold towards the round sphere, through an infinite dimensional evolution equation followed by a finite dimensional ``volume decreasing flow”. The latter can only be done within the framework of Sasaki geometry and is inspired by the work of MartelliSparksYau on volume minimization. Time permitting we will also talk about the case when the positivity assumption is replaced by nonnegativity. This talk is based on joint work with Weiyong He.
20120504T09:49:08+01:00
3679
1247661
true
16x9
false
no

Special Test Configurations (Chenyang Xu)
ucs_sms_1243544_1247343
http://sms.cam.ac.uk/media/1247343
Special Test Configurations (Chenyang Xu)
Tue, 24 Apr 2012 09:22:31 +0100
108
108104
Chenyang Xu
University of Cambridge
Dr J. Ross
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1a1ec8eaee86e5727a92a5774247f2dd
388e57f7142533a655c2afa94ae26f22
Cambridge University
3235
http://sms.cam.ac.uk/media/1247343
Special Test Configurations (Chenyang Xu)
(Joint with Chi Li) For any test configuration (TC) of a Fano manifold, we will use MMP theory to construct a new TC with the central fiber being a QFano variety (in particular it’s normal) such that the DonaldsonFutaki invariant of the new TC is smaller than the original one after scaling by the factor of the base change. We call a TC with a QFano central fiber a special TC. The above theorem gives an affirmative answer to Tian’s conjecture which says that to test K(semi)stability of a Fano manifolds, it suffices to only test on special TC.
20120424T10:34:12+01:00
3235
1247343
true
16x9
false
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Toric Slope Stability and Partial Bergman Kernels (Florian Pokorny)
ucs_sms_1243544_1247370
http://sms.cam.ac.uk/media/1247370
Toric Slope Stability and Partial Bergman Kernels (Florian Pokorny)
Tue, 24 Apr 2012 09:31:36 +0100
108
108104
Florian Pokorny
University of Cambridge
Dr J. Ross
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df7dee0d520fb87d1c0a2c5f20c7c99c
495862dcca438c64f9b3eef019cc8a17
Cambridge University
2310
http://sms.cam.ac.uk/media/1247370
Toric Slope Stability and Partial Bergman Kernels (Florian Pokorny)
In this talk, I will describe some recent work in collaboration with Michael Singer.
Let (L, h) \to (X, \omega) denote a polarized toric Kahler manifold. Fix a toric submanifold Y. We study the partial density function corresponding to the partial Bergman kernel projecting smooth sections of Lk onto holomorphic sections of Lk that vanish to order at least lk along Y for fixed l>0. I will explain how a distributional expansion of the partial density function (as k tends to infinity) can be used to give a direct proof that if \omega has constant scalar curvature, then (X,L) must be slope semistable with respect to Y. Finally, we will discuss some extensions of this result.
20120424T10:34:37+01:00
2310
1247370
true
16x9
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no
1243544