Time: Wednesday 4:00 pm (unless otherwise noted)

Schedule for the semester (Spring 2026)

Mar 11: Minsung Kim (POSTECH) 

Mar 25: Sovanlal Mondal (OSU) - 11 am

April 22: Jaelin Kim (Alfréd Rényi Institute of Mathematics)

May 6: Michael Bersudsky (Seoul National University)

May 20: Homin Lee (KIAS) 

3.11: Minsung Kim

Title: Rapid mixing for random walks on nilmanifolds.
Abstract: In chaotic systems, the mixing property is known for the fast decay of correlation. It is called rapid mixing if the correlation function decays super-polynomially. The mixing mechanism for hyperbolic systems and its compact group extensions were studied by Dolgopyat in a series of his papers in the late 90s'. 

In this talk, we prove rapid mixing for almost all random walks generated by $m\geq 2$ translations on an arbitrary nilmanifold. For several classical classes of nilmanifolds, we show m = 2 suffices. This provides a partial answer to the question raised in the work of Dolgopyat ('02) about the prevalence of rapid mixing for random walks on homogeneous spaces.

This is joint work with Dmitry Dolgopyat and Spencer Durham.

Mar 25: Sovanlal Mondal

Title: Ergodic averages along sequences of return times

Abstract: Motivated by Bourgain's return times theorem, recently, Donoso, Maass, and Arya-Saavedra studied ergodic averages along sequences generated by return times to shrinking targets in rapidly mixing systems. In this talk, we will show that their results can be improved to multiple ergodic averages for commuting transformations and a wider range of sequences.

This talk is based on joint work with Sebastián Donoso, and Vicente Saavedra-Araya.