Introduction to microlocal sheaves

Speaker:Michael McBreen (CUHK)

Time and place:

May 16, 2023, 15:20–16:55, Jinchun West Building, 3rd conference room,
May 18, 2023, 16:00-17:30,  Ning Zhai, W11,
May 23, 2023, 15:20–16:55, Jinchun West Building, 3rd conference room,
May 25, 2023, 16:00-17:30,  Ning Zhai, W11.


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.