From Lefschetz to String Topology

Join Moira Chas from Stony Brook University for a one-hour lecture exploring her mathematical journey from Lefschetz's fixed-point theorem to string topology. Discover how her early work on surface dynamics evolved into studying various aspects of curves on surfaces. Learn about the three key numbers determined by each free homotopy class of closed oriented curves on a Riemann surface: minimal self-intersection number, geometric length in hyperbolic metric, and word length relative to the fundamental group's generating set. Explore the Goldman Lie bracket of these classes and understand how these concepts can be computed or approximated using computational methods. Follow the intellectual path that ultimately led to the discovery of String Topology as Chas shares insights into the relationships between these mathematical concepts and their computational aspects.