Differential Geometry Working Seminar

Ravi Mudaliar, Department of Pure Mathematics, University of Waterloo

"A Categorical Equivalence between Compact Connected Riemann Surfaces and Function Fields in 1 variable"

I will discuss the interplay between analytic and algebraic data in the case of Riemann Surfaces. That is, to each Riemann Surface we can associate an algebraic object (function field) that completely encodes its analytic structure and given a function field we can associate a unique Riemann Surface (up to isomorphism) that completely encodes its algebraic structure. Throughout this construction I will also be proving some well-known facts about Riemann surfaces, such as the fact every compact connected Riemann Surface is an algebraic curve.

MC 5403