辛几何，切触几何，柏松几何系列报告1
时间： 2018 年6月8日，星期五
地点： 精正楼2楼报告厅
9:45-10:45 HongyuWang (Yangzhou University)
Title: OnNon-Elliptically Symplectic Manifolds
Abstract: In thistalk, we consider Euler numbers of non elliptically symplectic manifolds. Ourapproach is along the lines used by Gromov to give a proof of a vanishingtheorem for Kaehler hyperbolic manifolds.
11:10-12:10 WenchuanHu (Sichuan University)
Title: TheEuler number of an equivariant embedding into projective spaces
We will talk aboutthe Euler number of a projective variety C^*- equivariantly embedded into aprojective space is bounded by that of the projective space if the fixed pointset of the variety is finite, proposed by Carrell and Sommese.
14:00-15:00 Hitoshi Moriyoshi (Nagoya University)
Title: A newindex theorem on Fuzzy sphere
Abstract: In thelattice gauge theory there has been investigations to approximate the Diracoperator by finite dimensional objects. Fuzzy sphere, the endomorphism ring offinite-dimensional irreducible SO(3)-space, can be considered as one of suchattempts. However, the Fredholm index of an operator is uniquely determined inthe finite dimensional case, namely the difference of dimensions. In order toremedy the defect, Ginsparg and Wilson introduced a new relation to getnontrivial index. In this talk I shall explain about an explicit constructionof such operators and develop an index theorem on Fuzzy sphere. This is a jointwork with T. Natsume.
15:30-16:30 YunheSheng (Jilin University)
Title: CLWX2-algebroids and the first Pontryagin class of quadratic Lie algebroids
Abstract: We introduce the notion of a CLWX 2-algebroid(named after Courant-Liu-Weinstein-Xu) and study its properties. We give adetailed study on the structure of a transitive Lie 2-algebroid and describe atransitive Lie 2-algebroid using a morphism from the tangent Lie algebroid TM toa strict Lie 3-algebroid constructed from derivations. Then we introduce thenotion of a quadratic Lie 2-algebroid and define its first Pontryagin class, whichis a cohomology class in H^5(M). Associated to a CLWX 2-algebroid, there is aquadratic Lie 2-algebroid naturally. Conversely, we show that the firstPontryagin class of a quadratic Lie 2-algebroid is the obstruction class of theexistence of a CLWX-extension.