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Workshop on Extremal Kähler Metrics

and Stability

Edinburgh, 17-21 July 2006


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Scientific Programme and Participants

Workshop themes
The core topic of the workshop will be a natural generalization of the Aubin-Calabi-Yau metrics, extremal Kähler metrics. The existence problem for such metrics is a deep one, and certainly involves an interplay with nonlinear analysis on the one hand and the algebra-geometric notion of K-stability on the other. Related areas will also be considered, for example blow-up and desingularization theorems, the use of special techniques for the construction of examples of extremal Kähler metrics, and algebro-geometric theory of moduli of varieties.

Workshop structure
The Workshop starts with Registration (between 09.00 and 10.00) on Monday 17 July and finishes in the afternoon of Friday 21 July. There will be three one-hour lectures on most days, with ample time for discussion and contributed talks. A full programme will be posted on this page by June.

A link to expected participants can be found here.
For Programme click here.

Main speakers will include the following:
Valery Alexeev (Georgia)
Claudio Arezzo (Universita di Parma)
David Calderbank (York)
Simon Donaldson (Imperial)
Xiuxiong Chen (Madison)
Frances Kirwan (Oxford)
Claude LeBrun (SUNY Stony Brook)
Xiaonan Ma (École Polytechnique, Palaiseau)
Toshiki Mabuchi (Osaka)
Jacob Sturm (Rutgers)
Gang Tian (Princeton University)
Eckart Viehweg (Essen)
Ben Weinkove (Harvard)
Steve Zelditch (Johns Hopkins)

Provisional Programme

Monday 17 July
09.00-10.00 Registration and coffee
10.15-11.15 Steve Zelditch (Johns Hopkins University)
Geodesics in spaces of metrics on a toric variety
11.15-11.45 Coffee
11.45-12.45 Simon Donaldson (Imperial College London)
Extremal metrics on toric surfaces
12.45-14.30 Lunch in Exhibition Room, 14 India Street
14.30-15.30 Xiaowei Wang (Hong Kong)
Moment map in Riemannian geometry
15.30-16.00 Coffee
16.00-17.00 Simon Donaldson (Imperial College London)
Numerical solutions in Kähler geometry
17.30 Reception with wine, 14 India Street
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Tuesday 18 July
09.30-10.30 Frances Kirwan (University of Oxford)
Symplectic implosion and non-reductive quotients
10.30-11.00 Coffee
11.00-12.00 Eckhart Viehweg (University of Essen)
Compactification of base spaces of morphisms and of moduli schemes
12.00-14.00 Lunch break
14.00-15.00 Ben Weinkove (Harvard University)
Energy functionals in Kähler geometry
15.00-15.30 Coffee
15.30-16.30 Xiuxiong Chen (University of Wisconsin-Madison)
Geodesic ray, lower bound of geodesic distance and the Calabi energy
16.30-17.30 Gabor Szekelyhidi (Imperial College London)
The Calabi functional on a ruled surface
19.00 Group meal at Nargile, Hanover Street
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Wednesday 19 July
09.30-10.30 David Calderbank (University of York)
Projective bundles of order one
10.30-11.00 Coffee
11.00-12.00 Valery Alexeev (University of Georgia)
Branchvarieties and stable branchpairs
12.00 Free afternoon
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Thursday 20 July
09.30-10.30 Gang Tian (Princeton University)
Kähler-Ricci flow and minimal models
10.30-11.00 Coffee
11.00-12.00 Toshiki Mabuchi (University of Osaka)
Stabilities and extremal metrics for polarized algebraic manifolds
12.00-14.00 Lunch break
14.00-15.00 Xiaonan Ma (École Polytechnique, Palaiseau)
Asymptotic expansion of Bergman kernel, without or with group actions
15.00-15.30 Coffee
15.30-16.30 Julius Ross (Columbia)
Slope stability of polarised varieties
19.00 Workshop Dinner, Howies, Waterloo Place (dress informal)
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Friday 17 July
09.30-10.30 Claudio Arrezzo (Universita di Parma)
Extremal metrics and blow ups
10.30-11.00 Coffee
11.00-12.00 Jacob Sturm (Rutgers University)
Test configurations and geodesicsin the space of Kähler potentials
12.00-14.00 Lunch break
14.00-15.00 Claude LeBrun (SUNY Stony Brook)
The Einstein-Maxwell equations, extremal Kähler metrics, and Seiberg-Witten theory
15.00-15.30 Coffee
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Expected Participants

27 June

Name Institution
Abreu, Miguel Instituto Superior Tecnico
Alexeev, Valery University of Georgia
Apostolov, Vestislav University of Quebec at Montreal
Arezzo, Claudio Universita di Parma
Calderbank, David University of York
Chen, Xiuxiong University of Wisconsin-Madison
Dai, Xianzhe University of California, Santa Barbara
Donaldson, Simon Imperial College, London
Fine, Joel Imperial College, London
Futaki, Atiko Tokyo Institute of Technology
Gauduchon, Paul École Polytechnique et CNRS
Hwang, Andrew College of the Holy Cross
Keller, Julien Imperial College London
Kirwan, Frances University of Oxford
LeBrun, Claude SUNY Stony Brook
Ma, Xiaonan École Polytechnique, Palaiseau
Mabuchi, Toshiki University of Osaka
Marinescu, George Johann Wolfgang Goethe Universität
Maschler, Gideon Emory University
Pacard, Frank Université Paris 12
Panov, Dmitri Imperial College London
Paul, Sean University of Wisconsin-Madison
Phong, Duong Columbia University
Popovici, Dan University of Warwick
Rollin, Yann Imperial College, London
Ross, Julius Columbia University
Sano, Yuji IHES visitor
Simanca, Santiago University of New Mexico
Singer, Michael University of Edinburgh
Song, Jian Johns Hopkins University
Sturm, Jacob Rutgers University
Szekelyhidi, Gabor Imperial College, London
Thomas, Richard Imperial College, London
Tian, Gang Princeton University
Tonnesen-Friedman, Christina Union College
Viehweg, Eckart University of Essen
Wang, Xiaowei Chinese University of Hong Kong
Weinkove, Ben Harvard University
Zelditch, Steve Johns Hopkins University
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