Monday, April 18, 2022
Time | Items |
---|---|
All day |
|
10am |
04/18/2022 - 10:30am Let G be a geometrically finite subgroup of PSL(2,R). We say that a representation r from G to PGL(d,R) is a Hitchin representation if there is an r-equivariant positive map from the real projective line to the space of complete flags in R^d. We then prove a rigidity result for the entropy of Hitchin representations, generalizing previous work of Potrie-Sambarino. This is joint work with Richard Canary and Andrew Zimmer. Location:
Zoom
|
3pm |
04/18/2022 - 3:20pm We discuss topologically twisted five-dimensional SU(2) supersymmetric Yang-Mills theory on M4 x S1, where M4 is a smooth closed four-manifold. We provide two different path integral derivations of certain correlation functions, which can be identified with the K-theoretic version of the Donaldson invariants. In particular we derive their wall-crossing formula, first in the so-called U-plane integral approach and in the perspective of instanton counting. The result reproduces and generalizes the work of Gottsche, Nakajima, and Yoshioka in 2006. Location: |
4pm |
04/18/2022 - 4:00pm Location:
LOM 206
04/18/2022 - 4:00pm Abstract: Selberg’s 3/16 theorem for congruence covers of the modular surface is a beautiful theorem which has a natural dynamical interpretation as uniform exponential mixing of the geodesic flow. Bourgain-Gamburd-Sarnak’s breakthrough works initiated many recent developments to generalize Selberg’s theorem for infinite volume hyperbolic manifolds. One such result is by Oh-Winter establishing uniform exponential mixing of the geodesic flow for congruence covers of convex cocompact hyperbolic surfaces. We present a further generalization to higher dimensions for the frame flow which is a new result even for a single manifold. Immediate applications include an asymptotic formula for matrix coefficients with an exponential error term, exponential equidistribution of holonomy of closed geodesics, affine sieve, and a uniform resonance-free half plane for the resolvents of the Laplacians. Location:
LOM 215
|