辛几何，切触几何，柏松几何系列报告2
时间： 2018 年6月9日，星期六
地点： 精正楼2楼报告厅
9:45-10:45 ReyerSjamaar (Cornell University)
Title: Transversely symplectic Riemannian foliations
Abstract: Examplesof transversely symplectic Riemannian foliations include K-contact manifolds, cosymplecticmanifolds, symplectic mapping tori, and Prato's toric quasifolds. The leafspace of such a foliation is an étale symplectic stack. I will survey my recentwork with Benjamin Hoffman and Yi Lin about actions of Lie groups and Lie2-groups on such spaces, such as a convexity theorem and an
Atiyah-Bott-Berline-Vergnetype localization theorem.
11:10-12:10 YanliSong (Washington University in St.Louis)
Title: Recent progress on geometric quantization andreduction problems
Abstract: This is a expositorytalk about the quantization commutes with reduction theorem. I will also talkabout its various generalization and its application in index theory,representation theory, symplectic geometry etc.
14:00-15:00 DonghoonJang (Pusan National University)
Title: Fixedpoints of symplectic circle actions
Abstract: Duringthis talk, we consider a symplectic circle action that has fixed points. Wediscuss the classification of a symplectic circle action with fixed points,from small numbers of fixed points and from low dimensions. Next, we discusswhen a symplectic circle action is Hamiltonian.
15:20-16:20 XiaoshanLi (Wuhan University)
Title: On the stability of equivariant embeddingof CR manifolds with circle actions
Abstract: Thestability of embedding of compact strongly pseudoconvex CR manifold is relatedto the moduli space of the CR structures. Tanaka established any CR embeddingis stable when the dimension of the CR manifold is greater or equal to five andthe first Kohn-Rossi cohomology is invariant with respect to the deformation ofthe CR structures. However, examples of unstable embedding exist when thedimension is three. In this talk, on three dimensional CR manifold with circleaction we will show the equivariant embedding is stable under the$S^1$-invariant deformation of CR structure. This talk is based on a series ofjoint work with H. Herrmann, C.-Y. Hsiao and G. Marinescu.
16:30-17:30 ChenHe (Tsinghua University)
Title: Theequivariant cohomology ring of a cohomogeneity-one action
Abstract: A groupaction G action on M is a cohomogeneity-one action if its orbit space M/G isone-dimensional. We give a complete computation of the equivariant cohomologyring of such group action. (Joint with J. Carlson, O. Goertsches and L. Mare)