Title：Noncommutative moduli spaces
Reporter：Andrey Lazarev
Work Unit：Lancaster University
Time：2023/08/21-25
Address：Room 313, Zhengxin Building
Summary of the report:
The aim of this minicourse is to outline the construction of global moduli spaces of different objects of algebraic and geometric nature (such as flat connections in vector bundles, modules over associative algebras, objects in dg categories etc.) in a homotopy invariant context. The first part of the course will explain how local Koszul duality of Hinich and Keller-Lefevre provides a suitable context for studying local moduli problems (also known as deformations). The second part is devoted to the more recent work constructing the corresponding global theory. The global theory shares some properties with the local one, but involves several significantly new features, most notably the use of dg categories. The emphasis will be placed on explaining the conceptual picture rather than on technical proofs. Various instructive examples will be given.
Introduction of the Reporter: Andrey Lazarev is a professor at Lancaster University, UK, where he works on algebraic topology and homotopy theory. He is the editor-in-chief of Bull. Lond.Math.Soc. He has published many high-level papers in journals such as Adv. Math., Proc. Lond.Math. Soc., J. Noncommut.Geom.,etc.
