Talks

I will discuss a theorem, joint work in progress with Constantin Teleman, in which we characterize which topological 3-dimensional Chern-Simons theories admit nonzero boundary theories.  Accepting some physical heuristics, it tells which gapped systems in 2+1 dimensions admit only gapless boundary systems.

The event horizon and the Cauchy horizon of an extremal black hole admit conserved charges associated with scalar perturbations. We will see that these charges are externally measurable from null infinity. This suggests that these charges have the potential to serve as an observational signature for extremal black holes. The proof of this result is based on obtaining precise late-time asymptotics for the radiation field of outgoing perturbations.

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.