Thurston Elements in the Mapping Class Group

Explore a 59-minute lecture from the Joint IAS/PU Groups and Dynamics Seminar where Joseph Maher from The City University of New York discusses "Thurston Elements in the Mapping Class Group." Discover how Maher examines Thurston's explicit construction of pseudo-Anosov elements in the mapping class group of a compact surface, which uses Dehn twists in pairs of filling multicurves. Learn about the research findings showing that the probability of a random walk of length n on the mapping class group yielding an element with a power arising from Thurston's construction approaches zero as n increases to infinity. This mathematical exploration represents joint work with Jing Tao and will be presented at the Institute for Advanced Study on April 29, 2025, in Simonyi 101 at 4:30pm.