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Infinity categories and why they are useful, I

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

February 01, 2019 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Carlos Simpson (Universite de Nice Sophia Antipolis)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC



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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