L^2 moduli spaces of symplectic vertices

Written by：GAPA Last updated：2019-12-18

主题

活动时间

2019年11月25日 16:00 - 2019年11月25日 17:30

活动地址

Room 519 (New Math Building)

主讲人

Bohui Chen (Sichuan University)

In this talk, we will talk about the L2-moduli spaces of symplectic vortices on Riemann surfaces with cylindrical ends. Let (X,ω) be a compact symplectic manifold with a Hamiltonian action of a compact Lie group G and μ:X→g be its moment map. We studied a circle-valued action functional whose gradient flow equation corresponds to the symplectic vortex equations on a cylinder S1×R. Assume that 0 is a regular value of the moment map μ, we show that the functional is of Bott-Morse type and its critical points of the functional form twisted sectors of the symplectic reduction (the symplecitc orbifold [μ−1(0)/G]). We show that any gradient flow lines approaches its limit point exponentially fast. Fredholm theory and compactness property are then established for the L2-Moduli spaces of symplectic vortices on Riemann surfaces with cylindrical ends. This talk is based on a joint work with Bai Ling Wang.

Abstract: In this talk, we will talk about the L2-moduli spaces of symplectic vortices on Riemann surfaces with cylindrical ends. Let (X,ω) be a compact symplectic manifold with a Hamiltonian action of a compact Lie group G and μ:X→g be its moment map. We studied a circle-valued action functional whose gradient flow equation corresponds to the symplectic vortex equations on a cylinder S1×R. Assume that 0 is a regular value of the moment map μ, we show that the functional is of Bott-Morse type and its critical points of the functional form twisted sectors of the symplectic reduction (the symplecitc orbifold [μ−1(0)/G]). We show that any gradient flow lines approaches its limit point exponentially fast. Fredholm theory and compactness property are then established for the L2-Moduli spaces of symplectic vortices on Riemann surfaces with cylindrical ends. This talk is based on a joint work with Bai Ling Wang.