Riemann Surfaces
Andrew Monk
Friday 10th November, 2017 16:00-17:00 Maths 311B
Abstract
Riemann surfaces arise in many different branches of mathematics and physics. Originally, Riemann noticed that it is possible to replace the domain of certain complex functions (such as the complex logarithm) by a surface in natural way.
In this talk I will explain how basic examples of Riemann surfaces, such as the sphere and the torus, come from certain functions defined on the plane. I will also explain one of the key theorems in the theory of compact surfaces, the Riemann-Roch theorem.
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