Mathematics Colloquium Talk Series - Curve graphs and their variants: marrying topology and combinatorics using algebra

Abstract: Curve graphs of a surface are graphs that encode topological data about a surface and have been used to study many groups associated with surfaces. One such group is the mapping class group of a surface, which describes the symmetries of a surface. In this talk, we will establish the connection between topology and combinatorics by studying Ivanov's famed theorem: the automorphism group of the curve graph is naturally isomorphic to the (extended) mapping class group. We will then state Ivanov's metaconjecture on automorphism groups of curve graphs and explore recent developments in that direction.