Derived Equivalences from Variation of Lagrangian Skeletons

Abstract: A Lagrangian skeleton is a singular Lagrangian in a symplectic manifold, such that it has a tubular neighborhood as Weinstein manifold. One can associate a category (wrapped Fukaya category) to a Lagrangian skeleton, and study when does the category remain invariant as the Lagrangian varies. Many categories in mirror symmetry and representation theory can be described using such categories on Lagrangian skeletons, and it’s interesting to see how variation of skeleton induces derived equivalences between categories. I will begin with definition and basic examples, no prior knowledge of wrapped Fukaya category is needed. Some of the results are based on works arXiv:1804.08928, arXiv:2011.03719, arXiv:2011.06114 (joint with Jesse Huang).

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic