We give an elementary and self-contained proof of the uniformization theorem for noncompact simply connected Riemann surfaces.

We show that the higher genus 4-point superstring amplitude is strongly constrained by the geometry of moduli space of Riemann surfaces. A detailed analysis leads to a natural proposal which satisfies several conditions. The result is based on the recently derived Siegel induced metric on the moduli space of Riemann surfaces and on combinatorial products of determinants of holomorphic abelian d...

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.