Talks

Topology illuminates properties of geometric spaces which are independent of scale.  Scale-independent features of physical systems play an important role, for example when deducing the large-scale behavior from a small-scale description.  After an introduction to basic topological ideas, I will discuss two joint results with Mike Hopkins, one an application to string theory and the other an application to condensed matter theory.

Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this talk, we study the entanglement entropy of 2D topological phases from the perspective of quasiparticle fluctuations. In this picture, the entanglement spectrum of a topologically ordered system encodes the quasiparticle fluctuations of the system, and the entanglement entropy measures the maximal quasiparticle fluctuations on the entanglement boundary. As a consequence, entanglement entropy corresponds to the thermal entropy of the quasiparticles at infinite temperature on the entanglement boundary. We corroborates our results with explicit computation in the quantum double model with/without boundaries. We then systematically construct the reduced density matrices of the quantum double model on generic 2-surfaces with boundaries.