Raymond Cheng, Department of Pure Mathematics, University of Waterloo
“Moduli Space of Riemann Surfaces”
We have spent the last couple weeks studying the Teichmu ̈ller space, the study culminating in the finding that Teichmu ̈ller space is contractible. One important consequence of this result is that it gives a way to study certain topological and cohomological properties of quotients of the space. Of particular interest is the quotient by the Mapping Class Group; the resulting space is the moduli space of Riemann surfaces. We begin in this talk by discussing the moduli space of Riemann surfaces and by pointing toward some constructions we can perform in order to understand the topology of the moduli space.
MC 5403