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SCGP Weekly Talk: Anton Kapustin

Title: Statistical mechanics of fermions and topology of spin manifolds
Speaker: Anton Kapustin
Date: Tuesday, May 26, 2015
Time: 01:00pm – 02:00pm
Place: Lecture Hall 102, Simons Center

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Abstract: I will discuss models of statistical mechanics which involve integration over Grassmann variables. Such models have been proposed to describe phases of matter where the fundamental particles are fermions. I argue that all such models have ambiguities which can be resolved by introducing a simplicial analog of spin structure. This can be regarded as a version of the spin-statistics relation. Turning this around, statistical mechanics of fermions on a triangulated manifold provides a way to construct topological invariants of spin manifolds, such as equivariant spin cobordism classes and spin-Turaev-Viro invariants.