MINI COURSE Introduction to microlocal sheaves

Time & Venue

May 16, 2023, Tuesday, 15:20–16:55

Jinchun West Building, 3rd conference room

May 18, 2023, Thursday, 16:00-17:30

Ning Zhai, W11

May 23, 2023, Tuesday, 15:20–16:55

Jinchun West Building, 3rd conference room

May 25, 2023, Thursday, 16:00-17:30

Ning Zhai, W11

Speaker

Prof. Michael McBreen

The Chinese University of Hong Kong

Assistant Professor

BSc (McGill University)

PhD (Princeton University)

I study the intersection of representation theory, symplectic geometry and mathematical physics, focusing on conformal field theory, supersymmetric gauge theory and topological string theory.

Personal Website:

https://sites.google.com/view/mmcbreen/home

Abstract

Microlocal analysis was introduced by Sato in the 1960s as a way to study differential equations on manifolds 'locally on the cotangent bundle'. Many fundamental aspects of sheaf theory are best understood through this lens. More recently, work of Ganatra, Pardon and Shende (expanding on the results of Nadler and Zaslow for cotangent bundles) showed how microlocal sheaves can be used to describe the Fukaya category of a Weinstein manifold.

This minicourse will give an introduction to microlocal sheaves following Kashiwara and Schapira's classic Sheaves on Manifolds, with a focus on applications to geometric representation theory. We will study microlocalisation and micro-hom functors, functoriality with respect to symplectomorphisms and index theorems. We will consider a few suggestive examples where the category of microlocal sheaves can be described explicitly in terms of quiver representations. We will also look at more recent developments such as wrapped microlocal sheaves, microlocal sheaves on Weinstein manifolds and relationships to the Fukaya category.