14:15-15:15 Nándor Simányi (University of Alabama at Birmingham)
Abstract: In the 1980s M. P. Wojtkowski introduced an interesting dynamical system of 1D balls moving in a vertical half-line, colliding with each other and the hard floor elastically, and falling down under constant gravitation. To avoid the existence of linearly stable periodic orbits, one assumes that the masses of the particles are decreasing as we go up in the half line. He conjectured that all these systems are completely hyperbolic and ergodic.

Complete hyperbolicity of all such systems was shown by N. S. in 1996. Here we describe a brand new algebraic approach to such systems that enable us to verify all the conditions of the Local Ergodic Theorem for Dynamical Systems With Invariant Cone Fields (by Liverani and Wojtkowski) for almost all such falling ball systems, thus proving their ergodicity, a famous, so far unsolved conjecture of Maciej P. Wojtkowski from the mid 1980's.

In the talk special emphasis will be given to some interesting new aspects of the exploited algebraic approach that made it possible to prove the annoying
transversality condition (the equivalent of the Chernov-Sinai Ansatz for billiards) assumed in my conditional result [S2022].

[S2022] Simanyi, N.: "Conditional Proof of the Ergodic Conjecture for Falling Ball Systems". To appear in Contemporary Mathematics (2022),
https://arxiv.org/abs/2211.10874


15:30-16:30 Klaudiucz Czudek (IST Austria)
Title: Random walks in quasiperiodic environment
Abstract: We consider the environment viewed by the particle process in random walk in quasiperiodic environment. This process appears to be certain simply defined random walk on the circle. We prove the central limit theorem and establish the rate of mixing in the Diophantine case. This is based on a joint work with D. Dolgopyat.


17:00-18:00 Adam Kanigowski (Univ. of Maryland and Jagellonian Univ. krakow)
Title: Chaotic properties of smooth dynamical systems
Abstract: One of the central discoveries in the theory of dynamical systems was that differentiable (or smooth) systems can display strongly chaotic behavior and in many ways behave like a sequence of random coin tosses. In this talk we will describe the appearance and interactions of chaotic properties in smooth dynamics. We will highlight main developments, describe the state of the art and discuss some open problems in the field.