Monday, February 10, 2020
02/10/2020 - 4:00pm
We will discuss joint work with Hee Oh in which we establish exponential mixing of the geodesic flow for all geometrically finite hyperbolic (d+1)-manifolds with critical exponent greater than d/2. Key ingredients of our proof are the spectral gap of the Laplace operator on the manifold due to Lax-Phillips, and a careful study of the asymptotic behavior of matrix coefficients of complementary series representations of the special orthogonal groups SO(d+1,1).
02/10/2020 - 4:30pm
Factorization algebras provide a flexible language for describing the observables of a perturbative QFT, as shown in joint work with Kevin Costello. In ongoing work with Eugene Rabinovich and Brian Williams, we extend those constructions to a manifold with boundary for a special class of theories that includes, as an example, a perturbative version of the correspondence between chiral U(1) currents on a Riemann surface and abelian Chern-Simons theory on a bulk 3-manifold. Given time, I’ll sketch a systematic higher dimensional version for higher abelian CS theory on an oriented smooth manifold of dimension 4n+3 with boundary a complex manifold of complex dimension 2n+1; it has interesting relationship with the intermediate Jacobian.