Dr. Agnes Beaudry (Dept. of Mathematics, Univ. of Colorado Boulder)

09/30/2024  4:10pm

Abstract:

In recent years, there has been a growing number of applications of stable homotopy theory to condensed matter physics, many of which stem from a conjecture of Kitaev that gapped invertible phases of matter should be classified by the homotopy groups of a spectrum. This gives rise to a mathematical modeling question: how do we model quantum systems in such a way that this result can be better understood, perhaps even proved? In this mostly expository talk, I'll explain some aspects of Kitaev's conjecture and of this modeling problem and present some results in lowspacialdimensions.