Riemann Surfaces: Expanded Notes for a 25 Minute Talk

Introduction to Compact Riemann Surfaces

The theory of Riemann surfaces is a classical field of mathematics where geometry and analysis play equally important roles. The purpose of these notes is to present some basic facts of this theory to make this book more self contained. In particular we will deal with classical descriptions of Riemann surfaces, Abelian differentials, periods on Riemann surfaces, meromorphic functions, theta fun...

Speaker : Professor Kirti Joshi , University of Arizona Title : “ Vector Bundles on Curves : A Perspective ”

Vector bundles on Riemann surfaces (or algebraic curves) play an important role in the theory of Riemann surfaces and appear in many areas of mathematics and also mathematical physics. In this talk we will introduce the audience to some fascinating aspects of this beautiful subject. A large part of the talk is aimed at graduate students familiar with some topology/differential geometry.

Notes on Compact Riemann Surfaces

Riemann Surfaces and Their Moduli

The purpose of these notes is to give an overview of Riemann surfaces, and their moduli spaces. In general, theorems will be presented without proof, although references will be provided. These notes were originally prepared for the summer 2004 session of the UIUC Graduate String Seminar1. Proofs of nearly all the theorems may be found, unless otherwise noted, in [FK80]. CONTENTS 1. Mathematica...

Lectures on Moduli Spaces of Elliptic Curves

These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. 1 Their goal is to introduce and motivate basic concepts and constructions important in the study of moduli spaces of curves and abelian varieties through the example of elliptic curves. The advantage of working with elliptic curves is that most constructio...