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.
April 22: Jaelin Kim
Title: Uniform random walk on discrete graphs and loop processes
Abstract: In the finite graph, the maximal entropy random walk is well understood. In the ergodic-theoretic view point, it is the invariant measure of maximal entropy of the subshift of finite type over vertex set, induced by adjacency matrix. In this talk, we will introduce a generalization of MERW on infinite graphs, which we call a uniform random walk. By observing its behavior on graphs with weighted loops, we will see it gives meaningful notion even in the transient case.
May 6: Michael Bersudsky
Title: Dynamics in the moduli space of k-dimensional lattices in n-dimensional space
Abstract: I will consider the dynamics of linear groups acting on the moduli space of k-lattices in n-dimensional space. Specifically, the moduli space of k-lattices is the collection of rank-k discrete subgroups of $\mathbb{R}^n$ defined up to scaling. The action of matrix groups on this space combines features of the contracting dynamics on the Grassmannian with the expanding dynamics on the space of lattices.
I will talk about the number-theoretic motivation for considering this setup and present several recent and ongoing joint works concerning the norm-ball averages along orbits of certain discrete subgroups acting on this space.
May 20: Homin Lee
Title: Random dynamics on surfaces
Abstract: In this talk, we will consider random dynamical systems and group actions on surfaces that are given by diffeomorphisms. We will discuss about the absolutely continuity of stationary measures, the classification of orbit closures, and the exact dimensionality of stationary measures. This talk is mostly based on joint work with Aaron Brown, Davi Obata, and Yuping Ruan.