Equivariant Lagrangian Correspondence and a Conjecture of Teleman

Yan-Lung Leon Li

It has been a continuing interest, often with profound importance, in understanding the geometric and topological relationship between a Hamiltonian G-manifold Y and a symplectic quotient X. In this talk, we shall provide precise relations between their (equivariant) Lagrangian Floer theory. In particular, we will address a conjecture of Teleman, motivated by 3d mirror symmetry, on the 2d mirror construction of X from that of Y, which generalises Givental-Hori-Vafa mirror construction for toric varieties. The key technical ingredient is the Kim-Lau-Zheng’s equivariant extension of Fukaya’s Lagrangian correspondence tri-modules over equivariant Floer complexes. Joint work with Siu-Cheong Lau and Naichung Conan Leung.

https://www.ias.edu/video/equivariant-lagrangian-correspondence-and-conjecture-teleman