Random Walks and Asymptotic Geometry of Groups

Explore advanced topics in random walks and asymptotic geometry of groups through this comprehensive lecture series from the Institut Henri Poincaré's 2014 trimester program. Delve into cutting-edge research presented by leading mathematicians including Rostislav Grigorchuk on invariant random subgroups of lamplighter-type groups, Alex Lubotzky on quantum error correcting codes, and Amos Nevo on Diophantine approximation rates by lattice orbits. Examine spectral gap theory and random walks on Euclidean isometry groups with Elon Lindenstrauss, investigate free Engel groups with Elyahu Rips, and study sheaves on graphs and L^2 Betti numbers with Joel Friedman. Learn about metric ultraproducts of finite simple groups from John Wilson, explore embeddings in subexponential growth groups with Laurent Bartholdi, and discover Tarski numbers of groups through Mark Sapir's research. Investigate profinite isomorphism problems with Martin Bridson, study invariant random subgroups with Miklos Abert, and examine asymptotic dimensions of curve complexes with Mladen Bestvina. Explore innovative group theory constructions with Nicolas Monod, analyze right-angled cocompact lattices in higher rank simple Lie groups with Nikolay Nikolov, and study holomorphic families of Riemann surfaces from an asymptotic group theory perspective with Thomas Delzant. Additional topics include relative growth of subgroups with Alexander Olshanskii, outer space for right-angled Artin groups with Karen Vogtmann, relatively hyperbolic group actions with Leonid Potyagailo, random walks on p-adic flag varieties with Yves Benoist, envelopes and equivalence relations in free groups with Zlil Sela, and vertex finiteness for relatively hyperbolic groups with Gilbert Levitt.