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

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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