Full exceptional collections via window categories

This talk will focus on a particular structure of derived categories called a full exceptional collection. We will discuss the landscape of full exceptional collections and its connections to geometry, then explore how to produce them for linear GIT quotients using ideas from window categories and equivariant geometry. As an example, we will consider a large class of linear GIT quotients by a reductive group of rank two, where this machinery produces full exceptional collections consisting of tautological vector bundles. This talk is based on joint work with Daniel Halpern-Leistner.