Mathematics Department Colloquium: Two applications of topology to condensed matter physics

Colloquium | January 30 | 4:10-5 p.m. | 60 Evans Hall

 Daniel S. Freed, University of Texas at Austin

 Department of Mathematics

In recent years there have been novel uses of topological ideas and methods to problems in condensed matter physics. For example, phases of matter are path components of a moduli space of quantum systems, and since the set of path components is homotopy invariant one can approach the classification of phases with "soft methods".

In joint work with Mike Hopkins we compute the homotopy type of spaces of invertible field theories and apply the result to this problem. In another direction, in ongoing work with Constantin Teleman, we use topological field theory to find a criterion which tells that certain 2-dimensional insulators are forced to have conduction on the edge.