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Exceptional Collections and Window Categories 

Kimoi Kemboi (IAS)
Tuesday, December 5, 2023 - 1:45pm
PDL C-38
Pre-talk: What is a Phantom?
Abstract: We will review key features of derived categories and introduce a mysterious class of subcategories called phantoms.
Title: Exceptional Collections and Window Categories 
Abstract: The derived category of a variety is a crucial algebraic invariant with several profound implications on the geometry of the underlying variety. 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 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. 
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