Symmetries and deformation invariants in quantum mechanics

Mathematical Conversations
Topic:Symmetries and deformation invariants in quantum mechanics
Speaker:Daniel Freed
Affiliation:University of Texas at Austin; Member, School of Mathematics and Natural Sciences
Date:Wednesday, March 4
Time/Room:6:00pm - 7:00pm/Dilworth Room

I begin with a geometric discussion of Wigner's theorem concerning the linearization of quantum mechanical symmetries; it first appeared in a joint paper with von Neumann. This is the starting point for joint work with Gregory Moore in which we first explain how 10 symmetry classes of quantum mechanical systems come about. Then I'll explain how for free electron systems various forms of topological K-theory classify deformation classes (topological phases of matter). Little to no physics knowledge is required to follow the talk.