报告人：Anton Alekseev（University of Geneva）
时间：10月13日10:00-12:00 地点：智华楼王选报告厅-101
时间：10月15日10:00-12:00 地点：智华楼109室
时间：10月17日10:00-12:00 地点：智华楼王选报告厅-101
Abstract: Hamiltonian actions of infinite dimensional groups are of importance in field theory, and in particular in gauge theory. In this series of talks, we will consider examples of Hamiltonian actions of loop groups and of diffeomorphisms of the circle. The outline of the program is as follows.
Lecture 1: We will recall the main facts about Hamiltonian actions of compact groups on symplectic manifolds. These include the Marsden-Weinstein reduction, the convexity properties due to Atiyah and Guillemin-Sternberg (abelian case) and Kirwan, the Duistermaat-Heckman localization, the Kirwan’s surjectivity theorem, and the Guillemin-Sternberg quantization commutes with reduction (or [Q,R]=0) principle.
Lecture 2: We will explain how the properties listed above generalize to Hamiltonian actions of central extensions of loop groups. This theory started around 30 years ago in the works of Meinrenken-Woodward, and by now it is almost complete. Among other things, it includes a theory of Lie group valued moment maps providing finite dimensional proxies of infinite dimensional Hamiltonian actions of loop groups.
Lecture 3: We will address the theory of Hamiltonian actions of the central extension of group of diffeomorphisms of the circle motivated by recent advances in Jackiw-Teitelboim 2-dimensional gravity.
报告人简介：Alekseev教授是数学物理、辛几何与李理论领域专家，2014年国际数学家大会邀请报告人，担任欧洲数学会杂志主编，相关工作发表在Ann. of Math, Invent. Math., Publ. Math. IHES等杂志。
