Geometry Working Seminar

Henry Lui, Department of Pure Mathematics, University of Waterloo

“Teichmu ̈ller Spaces”

Teichmu ̈ller theory studies complex structures on surfaces, most of which have hyperbolic geometry. So I will begin with some preliminaries on surfaces and hyperbolic geometry before motivating and defining Teichmu ̈ller spaces and mapping class groups, the main players in the theory. Since most of Teichmu ̈ller theory focuses on the ”general” case of negative Euler characteristic, I will explicitly compute the Teichmu ̈ller space of the torus for completeness, before we move onward.

MC 5403