Dynamics - Topology and Numbers

Explore advanced mathematical concepts through this comprehensive lecture series from the Hausdorff Center for Mathematics' trimester program on Dynamics: Topology and Numbers. Delve into cutting-edge research presented by leading mathematicians including Manfred Einsiedler's five-part series on Effective Homogeneous Dynamics, Alex Gorodnik's continuation of homogeneous dynamics theory, and Omri Sarig's extensive five-lecture exploration of the Transfer Operator Method. Examine specialized topics such as Don Zagier's work on holomorphic quantum modular forms, Frédéric Naud's research on spectral gaps of random covers of hyperbolic surfaces, and Hans Henrik Rugh's presentation on regularized Fredholm determinants. Study dynamical systems through Manfred Denker's analysis of toral automorphisms driven by continued fractions, Michael Baake's cocycle approach to Fourier transforms of Rauzy fractals, and Michael Magee's thermodynamical formalism applied to Markoff-Hurwitz equations. Investigate flow dynamics with Jon Chaika's five-part series on horocycle flow on moduli spaces of translation surfaces, alongside contributions from Mike Todd on escape of entropy and Oscar Bandtlow on spectral approximation of transfer operators. Learn about Diophantine approximation through Osama Khalil's work on fractals and homogeneous flows, Pengyu Yang's research on equidistribution of expanding translates, and Weikun He's analysis of linear random walks on the torus. Discover recent developments in number theory and dynamical systems through presentations by Taylor McAdam on almost-prime times in horospherical flows, Maxim Kirsebom's limiting distribution studies, and Manuel Luethi's work on joinings of diagonal flows with applications to elliptic curves.