Events for 04/30/2025 from all calendars

Groups and Dynamics Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Alain Valette, Université de Neuchâtel

Title: Reciprocal hyperbolic elements in PSL_2(Z)

Abstract: An element A in PSL_2(Z) is hyperbolic if |Tr(A)|>2. The maximal virtually abelian subgroup of PSL_2(Z) containing A is either infinite cyclic or infinite dihedral; say that A is reciprocal if the second case happens (A is then conjugate to its inverse). We give a characterization of reciprocal hyperbolic elements in PSL_2(Z) in terms of the continued fractions of their fixed points in P^1(R) (those are quadratic irrationals). Doing so we revisit results of P. Sarnak (2007) and C.-L. Simon (2022), themselves rooted in classical work by Gauss and Fricke & Klein.

Retirement Reception

Time: 3:30PM - 4:30PM

Location: Blocker 140

Description: Retirement Reception for Emil Straube, Edriss Titi and Jianxin Zhou retiring during summer 2025. We will also recognize Raytcho Lazarov's contributions to the department in memoriam.

Free Probability and Operators

Time: 4:00PM - 5:00PM

Location: BLOC 306

Speaker: Ping Zhong, University of Houston

Title: Brown measure of a free sum X+Y

Abstract: Brown measure is a sort of spectral measure for free random variables, not necessarily normal. I will report a joint work with Hari Bercovici on the Brown measure of a sum X+Y of two free non-selfadjoint random variables X and Y, where Y is R-diagonal. The procedure relies on studying free convolution of two symmetric measures and subordination functions. The Brown measure can predict the limiting eigenvalue distribution of full rank deformed single ring random matrix model.