2022/2023

Introduction to Riemann Surfaces

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Alexandr Buryak

Language: English

ECTS credits: 6

Contact hours: 72

Course Syllabus

Abstract

A Riemann surface is a two-dimensional manifold (surface) with a given complex structure. Remarkably, the theory of Riemann surfaces is full of beautiful results and at the same time the proofs do not require a lot of prior knowledge, particularly comparing with the theory of complex manifolds of higher dimension. Sheaf cohomology will be the main technical tool for us, and we will carefully derive all the necessary results from it. The main goal of the course is to derive the Riemann-Roch theorem, the Serre duality, and the Abel theorem.