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Infinity categories and why they are useful, III

Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces January 31, 2019 - February 08, 2019

February 05, 2019 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Carlos Simpson (Universite de Nice Sophia Antipolis)
Location: SLMath: Eisenbud Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

13-Simpson

Abstract

In this series, we'll introduce infinity categories and explain their relationships with triangulated categories, dg-categories, and Quillen model categories. We'll explain how the infinity-categorical language makes it possible to create a moduli framework for objects that have some kind of up-to-homotopy aspect: stacks, complexes, as well as higher categories themselves. The main concepts from usual category theory generalize very naturally. Emphasis will be given to how these techniques apply in algebraic geometry. In the last talk we'll discuss current work related to mirror symmetry and symplectic geometry via the notion of stability condition. 

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Video/Audio Files

13-Simpson

H.264 Video 862_25956_7594_13-Simpson.mp4
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