Thursday, November 30, 2023
Time  Items 

All day 

4pm 
11/30/2023  4:00pm Let F be a family of finite coverings of a hyperbolic surface S. A spectral gap of F is an interval I = [0, epsilon] such that the eigenvalues in I (counted with multiplicity) of the Laplacian \Delta_S of S and \Delta_X, any X ∈ F, are the same. I will present a joint work with M. Magee where we give a spectral gap for congruence coverings when S is the surface associated to a Schottky subgroup of SL(2, Z) with thick enough limit set. The proof exploits the link between eigenvalues of the Laplacian and zeros of dynamical zeta functions attached to S via the thermodynamic formalism. Location:
KT205
11/30/2023  4:00pm This is 11th lecture in the series. Location:
KT 801

9pm 
11/30/2023  9:00pm Falconer’s distance set conjecture says that a compact set in $\mathbb{R}^d$ whose Hausdorff dimension larger than $d/2$ must have a distance set of positive measure. The conjecture is still open in all dimensions. In this talk, I’ll discuss some recent progress towards it in dimension three and higher, which involves new techniques from the theory of radial projections and decoupling. This is based on joint works with Xiumin Du, Kevin Ren, and Ruixiang Zhang. Location:
KT 219
