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“Higher Structures and Symplectic Geometry”学术会议
作者:    时间:2018-04-28 浏览次数:

  

会议地点: 河南大学数学与统计学院一楼报告厅

活动时间: 2018年5月12日

 

内容简介:本次在河南大学举办的“Higher Structures and Symplectic Geometry”小型学术会议,由清华大学陈酌教授,中国农业大学郎红蕾教授,北京大学刘张炬教授,美国宾夕法尼亚州立大学徐平教授联合组织,旨在促进国内外在几何物理和数学物理研究领域的交流与合作。

 

参会嘉宾/单位:

Ruggero Bandiera教授 /意大利罗马第一大学(Sapienza University of Rome)

 

Pantelis Damianou教授 /塞浦路斯大学(University of Cyprus)

 

李慧(Hui Li)教授 /苏州大学(Soochow University)

 

林宗柱(Zongzhu Lin)教授 /河南大学(Henan University) & 美国堪萨斯州州立大学(Kansas State University)

 

刘张炬(Zhangju Liu)教授 /北京大学(Peking University)

 

潘日新(Yat Sun Poon) 教授 /美国加州大学河滨分校(University of California, Riverside)

 

Tudor Ratiu教授 /瑞士洛桑联邦理工大学(Swiss Federal Institute of Technology in Lausanne) & 上海交大(Shanghai Jiao Tong University)

 

Mathieu Stienon教授 /美国宾州州立大学(Penn State University)

 

吴可(Ke Wu)教授 /首都师范大学(Capital Normal University)

 

吴泉水(Quanshui Wu)教授 /复旦大学(Fudan University)

 

徐平(Ping Xu)教授 /美国宾州州立大学(Penn State University)

 

Francois Ziegler教授 /美国佐治亚南方大学(Georgia Southern University)

报告安排: 5月12日上午, 数学与统计学院一楼报告厅

 

8:45am: Openning 领导和嘉宾讲话

9:00am-9:50am Mathieu Stienon (Penn State University)

10:00am-10:50am Wei Hong (Wuhan Univerisity)

11:10am-12:00am Pantelis Damianou (University of Cyprus)

报告题目和摘要:

 

Mathieu Stienon

 

Title: Formality Theorem for Differential Graded Manifolds

 

 

Abstract: The Atiyah class of a dg manifold (M,Q) is the obstruction to the existence of an affine connection that is compatible with the homological vector field Q. The Todd class of dg manifolds extends both the classical Todd class of complex manifolds and the Duflo element of Lie theory.

 

Using Kontsevich's famous formality theorem, Liao, Xu and I established a formality theorem for smooth dg manifolds: given any finite-dimensional dg manifold (M,Q), there exists an L_oo quasi-isomorphism of dglas from an appropriate space of polyvector fields endowed with the Schouten bracket [-,-] and the differential [Q,-] to an appropriate space of polydifferential operators endowed with the Gerstenhaber bracket [[-,-]] and the differential [[m+Q,-]], whose first Taylor coefficient (1) is equal to the composition of the action of the square root of the Todd class of the dg manifold (M,Q) on the space of polyvector fields with the Hochschild--Kostant--Rosenberg map and (2) preserves the associative algebra structures on the level of cohomology.

 

 

Wei Hong

 

Title: Poisson Cohomology of Holomorphic Toric Poisson Manifolds

 

Abstract: A holomorphic toric Poisson manifold is a smooth toric variety, equipped with a holomorphic Poisson structure, which is invariant under the torus action. In this talk, we describe the Poisson cohomology groups of holomorphic toric Poisson manifolds. And we will explain our theory in the cases of CP^n and C^n.

 

 

Pantelis Damianou

 

Title: Transverse Poisson Structures and Kleinian Singularities

 

Abstract: We give a brief general review of the ADE classification problem. The survey includes simple Kleinian singularities, symmetries of Platonic solids, finite subgroups of SU(2), the Mckay correspondence, integer matrices of norm 2 and Brieskorn’s theory of subregular orbits. We conclude with some joint work with H. Sabourin and P. Vanhaecke on transverse Poisson structures to subregular orbits in semisimple Lie algebras. We show that the structure may be computed by means of a simple Jacobian formula, involving the restriction of the Chevalley invariants on the slice. In addition, using results of Brieskorn and Slodowy, the Poisson structure is reduced to a three dimensional Poisson bracket, intimately related to the simple rational singularity that corresponds to the subregular orbit. Finally we present some recent results on the minimal orbit.

 

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