November 12, 2019

Talks from 1:00-5:00 pm

Lunt Hall, Room 105,  Northwestern University

Reception and light dinner and at 5:00 pm

 

Schedule of Talks

1:00,  Holly Krieger (Cambridge)

Title: Thurston eigenvalues in complex dynamics

Abstract: To any rational map of the Riemann sphere, we can associate a collection of invariants given by the eigenvalues of the associated pushforward operator on the space of quadratic differentials with simple poles.  Recently, Buff-Epstein-Koch proved that many of the resulting invariants are dynamical; in particular, they arise from multipliers of periodic cycles of . We will discuss the possible dynamical significance of the remaining invariants, focusing on a family of quadratic rational maps.

2:30,  Wenyu Pan (UoC)

Title: Kleinian Schottky groups, Patterson-Sullivan measures, and Fourier decay

Abstract: We will start with the notion of Fourier dimension of a subset of . We will then focus on the particular case of the limit set of Kleinian Schottky groups and show the Fourier transform of the associated Patterson-Sullivan measures enjoy polynomial decay. This generalizes a result of Bourgain-Dyatlov for convex cocompact Fuchsian groups. The proof includes an estimate on the decay of exponential sums based on Bourgain-Gamburd sum-product estimate on and a regularity estimate for stationary measures for certain random walks on linear groups. This is a joint work with Jialun Li and Frédéric Naud.

4:00,  Alex Furman (UIC)

Title: Super-rigidity, Weyl groups, and hyperbolic structures

Abstract: We will discuss some super-rigidity results in the “higher-rank to hyperbolic-like target” paradigm, and show how to apply them to a geometric question of classifying hyperbolic structures on some groups.

Based on joint works with U.Bader, and another one with U.Bader. P.-E. Caprace, A. Sisto.

5:00,  Dinner