Geometry MMA Seminar: Geometric finiteness in mapping class groups

Speaker:  Teddy Weisman (UVA)

Title: Geometric finiteness in mapping class groups

Abstract:   The mapping class group Mod(S) of a finite-type surface S acts on the Teichmuller space of S; while Teichmuller space is not hyperbolic, the action has many interesting (but subtle) "hyperbolic-like" properties. Convex cocompact subgroups of Mod(S) are those whose action is the "most hyperbolic." Such subgroups have many equivalent characterizations in close analogy with different definitions of convex cocompact Kleinian groups, and they are intimately tied to the theory of surface bundles. There have been recent efforts to develop a broader theory of "geometrically finite" subgroups of the mapping class group; in this talk, I will discuss some work in progress with Spencer Dowdall and Sara Maloni towards one possible version of this theory. We give a definition of geometric finiteness that can be stated using either Teichmuller geometry, topological dynamics, or the geometry of the curve complex; we also introduce several new techniques to study the equivalences between these perspectives for our class of subgroups, which may have wider application.

Time:  Friday, October 30, 2026 – 1:30pm - 2:30pm

Place: Exploratory Hall, Room 4208