Orderability and Mapping Class Groups in Surface Topology

Explore a rigorous mathematical lecture on orderability and mapping class groups presented by Tyrone Ghaswala from the University of Waterloo. Delve into the fascinating rigidity result by Kathryn Mann and Maxime Wolff concerning circular orderings of the mapping class group of a once-punctured finite-type surface. Discover two key applications of this result: first, learn about the computation of the obstruction spectrum, which quantifies how much the once-punctured mapping class group fails to be left-orderable. Second, examine the relationship between translation numbers of elements in the mapping class group of a compact surface with one boundary component and their fractional Dehn twist coefficients. Gain insights into this collaborative research conducted with Adam Clay, expanding your understanding of advanced concepts in topology and group theory.