IHP trimester on random walks and dynamics
Paris , April - July 2028
Organized by
Timothée Bénard, Valérie Berthé, Anna Erschler, Péter Varjú, Tianyi Zheng
Thematic overview: The trimester will explore the deep connections between random walks, group theory, and dynamical systems, bringing together probabilistic, geometric, and algebraic perspectives. Central themes include random walks on finite and infinite groups, boundary theory, harmonic functions, homogeneous dynamics, harmonic analysis, continued fractions, and symbolic dynamics. The programme will further highlight the rich interplay with number theory, computer science, and aperiodic order, where random and dynamical methods have recently driven remarkable advances.
Schedule: The programme will run over a 12-week period. It will begin with a one-week introductory school for early-career researchers, held at CIRM (Luminy) in late April 2028. This will be followed by three one-week workshops at IHP (Paris), scheduled between May and mid-July. Between the workshops, weekly thematic activities will take place at IHP, including seminars and mini-courses led by distinguished researchers.
Workshop 1: Groups and symbolic dynamics.
The topics of this conference include subshifts over groups, groups as classification invariants, algebraic dynamics for abelian and non-abelian groups, equidistribution results and limit theorems for ergodic sums, continued fractions and homogeneous dynamics.
Workshop 2: Random walks on algebraic and geometric structures.
The topics of this conference include random walks on groups, Poisson boundary, Martin boundary, capacity of random walk range, transition probabilities estimates, spectral estimates, amenability, sofic approximations, pivoting points, mixing and the cut-off phenomenon.
Workshop 3: Random walks and effective dynamics.
The topics of this conference include random walks and flows on homogeneous spaces, stationary measures (dimension, absolute continuity, and Fourier decay), projection theorems.