國立清華大學 數學系

Abstract: 

Roughly speaking, algebraic geometry is a branch of mathematics which originated from studies of (geometric) properties of sets described by polynomial equations. Intimate interplay between analysis, algebra, and geometry have been happening frequently in this area and have brought very fruitful developments. In this talk, I will briefly introduce the notion of Riemann surfaces, one of the main sources of thoughts in algebraic geometry. I will exhibit some basics with a focus on the Riemann-Roch theorem, which establishes a fundamental relation between the genus of a compact Riemann surface and how many meromorphic functions and meromorphic 1-forms that Riemann surface have satisfying certain prescribed singularity conditions.