Seminar| Institute of Mathematical Sciences
Time: Thursday, January 02th, 2025,16:00-17:00
Location: IMS, RS408
Speaker:Yuan Gao, The University of Georgia
Abstract：A distinguished feature of Fukaya categories is that they often come with duality, given by various versions of Calabi-Yau structures which differ in the compact and open cases. For a Liouville manifold, the Rabinowitz Fukaya category is a relatively novel A-infintiy category whose morphism space is of Tate type, which measures the failure of Poincare duality for the wrapped Fukaya category, the latter having a weak smooth Calabi-Yau structure. The feature of the construction makes it difficult to access duality for the Rabinowitz Fukaya category itself. In this talk, I will discuss an algebraic approach to studying dualities for certain A-infinity categories via an analogue of residue in complex analysis and algebraic geometry, and explain how this leads to a weak proper Calabi-Yau structure of dimension one less on the Rabinowitz Fukaya category.