Dr. David Ayala (Dept. of Mathematical Sciences, MSU)

9/25/2023  4:10pm

Abstract: Confining electrons to 2-dimensional substrates results in new types of (quasi-)particles — anyons — which obey peculiar spin statistics.  Propagation of anyons form tangles in 3-space, operations upon which can be organized as a braided monoidal category.  I’ll explain a construction — factorization homology — that integrates a braided monoidal category over a 3-manifold M resulting in the home of all observables of an anyon system in M.  Factorization homology is an enhancement of Skein modules, and can be used to recover the Jones polynomial, as I’ll explain.