第七届清华三亚国际数学论坛-大师讲座--Claire Voisin超开勒流形,霍奇理论和周氏群研讨会(Master Lectures-- Hyper-Kaehler Manifolds, Hodge Theory and Chow Groups: Claire Voisin)

2016-12-19 ~ 2016-12-23 1641

synopsis and organizers

Synopsis: The subject lies at the interface of algebraic geometry and analytic geometry. Projective K3 surfaces have been studied since the nineteenth century, and they still hold a privileged place in algebraic geometry. K3 surfaces are nothing else but compact hyperkaehler manifolds of (complex) dimension 2. Higher dimensional compact hyperkaehler manifolds have been seriously studied only after Yau's solution of Calabi's conjecture. Interesting classes of examples hyperkaehlers have been produced, and a series of beautiful general results have been proved, but it is clear that what we know is only the tip of the iceberg. It is a remarkable fact that all known examples have been constructed by algebraic geometry methods while the available general results concerning the topology of these varieties and their moduli spaces pass through uniformization and thus are not actually algebraic. In the projective setting, the study of projective hyperkaehlers has used in a complementary way methods from Hodge theory, derived categories, and algebraic cycles and from any of these viewpoints, these varieties have very special properties, not yet fully understood. The subject is closely related to moduli spaces of sheaves, as most known examples have been constructed as moduli spaces.

Voisin will lecture on Chow rings of hyperkaehler's, a subject which has started with Beauville-Voisin's conjectures and will be central in the workshop. Other important topics covered in the workshop are derived category methods in the study of hyperkaehler's, applications of Hodge theory to geometry, and construction methods for hyperkaehler's.


Organizers

Name University
Claire Voisin Centre National de la Recherche Scientifique, France
Radu Laza Stony Brook University, USA
Kieran G. O'Grady Università degli Studi di Roma La Sapienza, Italy

participants

Ekaterina Amerik Université de Paris-Sud, France
Arend Bayer The University of Edinburgh, UK
Francois Charles Université de Paris-Sud, France
Baohua Fu Chinese Academy of Sciences, China
Lie Fu Université Claude Bernard Lyon 1, France
Zhi Jiang Shanghai Center for Mathematical Sciences
Ljudmila Kamenova Stony Brook University, USA
Radu Laza Stony Brook University, USA
Zhiyuan Li Stanford University, USA
Wenfei Liu Xiamen University, China
*Eduard J.N.Looijenga Universiteit Utrecht, Netherlands
Eyal Markman University of Massachusetts, USA
Giovanni Mongardi University of Bologna, Italy
Shigeru Mukai Kyoto University, Japan
Kieran G. O'Grady Università degli Studi di Roma La Sapienza, Italy
Gianluca Pacienza Université de Strasbourg et CNRS, France
Antonio Rapagnetta Università degli Studi di Roma Tor Vergata, Italy
Ulrike Riess Universität Bonn, Germany
Giulia Sacca Stony Brook University, USA
Mingmin Shen University of Amsterdam, Netherlands
Misha Verbitsky Russian National Research University "Higher school of economics"
Jaroslaw A. Wisniewski Warsaw University, Poland
Qizheng Yin Eidgenössische Technische Hochschule Zürich, Switzerland

Schedule

The Schedule for the Master Lectures-- Hyper-Kaehler Manifolds, Hodge Theory and Chow Groups.pdf

Titles and Abstracts

Titles and Abstracts for Hyper-Kaehler Manifolds, Hodge Theory and Chow Groups.pdf

Group Photos

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2017年度邵逸夫数学科学奖 http://www.shawprize.org/en/shaw.php?tmp=3&twoid=104&threeid=268&fourid=510