AG Seminar: Full exceptional collections on rank-two linear GIT quotients

A full exceptional collection is an important structure on a derived category with many valuable implications. For instance, such a collection produces a basis for the Grothendieck group. After reviewing the landscape of full exceptional collections on linear GIT quotients, we will discuss how to produce them using ideas from "window" categories and equivariant geometry. As an application, we will consider a large class of linear GIT quotients by a reductive group G 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.