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Explore the intersection of geometric group theory and homotopy theory in this 53-minute mathematical lecture delivered by Ulrike Tillmann from the University of Oxford at the Fields Institute. Delve into the fundamental connections between geometric properties of groups and their topological manifestations through homotopy-theoretic methods. Examine how geometric group theory concepts such as quasi-isometry, growth rates, and asymptotic properties relate to homotopy invariants and topological spaces. Investigate the role of classifying spaces, group cohomology, and K-theory in understanding geometric groups from a homotopy-theoretic perspective. Discover applications of these connections to problems in both geometric group theory and algebraic topology, including the study of mapping class groups, arithmetic groups, and their associated moduli spaces. Learn about recent developments in the field that bridge discrete geometric structures with continuous topological phenomena, providing insights into both the algebraic and topological properties of groups.
