Back to Departmental Colloquium: Fall 2025
Departmental Colloquium
Date: Thursday, Dec 4, 2025
Time: 4:00PM - 5:00PM
Location: JWB 335
Jing Tao
University of Oklahoma
Title |
From 2×2 matrices to infinite-type surfaces |
Abstract |
To every topological surface one can associate a group called the mapping class group (sometimes called the modular group), consisting of homeomorphisms of the surface up to isotopy. In the case of the torus, this group is SL(2,ℤ), whose elements fall into three dynamical types detected by the trace: elliptic (|tr A| 2). Remarkably, Thurston showed that an analogous classification exists for maps of finite-type surfaces: after cutting along a canonical multicurve, each component carries a map that is either periodic or pseudo-Anosov, and the map is reducible precisely when the reducing multicurve is nonempty. In this talk, I will first present these classical examples—from the linear case of 2×2 matrices to the nonlinear case of finite-type surfaces—before discussing joint work with Mladen Bestvina and Federica Fanoni, where we investigate how this classification extends (or fails) for more general surfaces. Spring 2026 |
Geometry and Topology