Prof.ssa Corinna Ulcigrai (Institut für Mathematik - Universität Zürich)
"Periodic surfaces and deterministic random walks: dynamics between geometry and probability"
Abstract: Many deterministic systems display chaotic features: the stronger the chaotic features, the better the system
can be approximated by a probabilistic model, an idea that can be traced back to Boltzmann and explains the success
of the branch of dynamical systems known as ergodic theory. In this talk, we will discuss systems that display only 'mild’
chaotic features, such as the geodesic flow on surfaces with a flat geometry or the Ehrenfest model in mathematical physics.
Recent breakthroughs in our understanding of the latter model introduced more than a century ago, were made possible by
the powerful tools exploiting moduli spaces of surfaces and Teichmueller dynamics, an area which has attracted the work
of several Fields medallists. We will in particular highlight some results of probabilistic flavor that can still be proven for these
deterministic systems, hidden in the fractal structure of trajectories and the 'deterministic random walks' that describe them.