Riemann-Roch and Elliptic Curves

Wednesday, January 18, 2017 - 16:00 to 16:50
Thackeray 427
Speaker Information
Jacob Gross
University of Pittsburgh

Abstract or Additional Information

The Riemann-Roch theorem (for compact Riemann surfaces) is a deep connection between complex analysis and topology. It states roughly that the behavior of functions, with prescribed analytic properties, on a surface is constrained by the genus of that surface. We prove this theorem and give an application – that nonsingular projective algebraic curves of genus one (e.g. elliptic curves) are described by cubic equations.