Arun Debray (UT-Austin) Modeling invertible TQFT using homotopy theory @Harvard CMSA 7/08/2021

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7/08/2021
Arun Debray (UT-Austin to Purdue)
Title: Modeling invertible topological phases of matter using homotopy theory

Abstract: Condensed-matter theorists have discovered examples of physical systems with unusual behavior, such as pointlike excitations that behave neither as bosons nor as fermions, leading to the idea of topological phases of matter. Classifying the possible topological phases has been the focus of a lot of research in the last decade in condensed-matter theory and nearby areas of mathematics. In this talk, I’ll focus primarily on the special case of invertible phases, also called symmetry-protected topological (SPT) phases, whose classification uses techniques from homotopy theory. I will discuss two different approaches to this, due to Kitaev and Freed-Hopkins, followed by details of the homotopy-theoretic classifications. The latter includes work of Freed-Hopkins and of myself.