2023/2024

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

The aim of the course is to demonstrate how some of the key ideas of algebraic geometry work, using the approach that does not require a hard technical introduction. With this aim in mind, the course is mainly concentrated on compact Riemann surfaces. Assuming Riemann's existing theorem without proof (in the form that any compact Riemann surfacecan be represented as a ramified covering of the extended complex plane corrseponding to an algebraic equation), we prove Riemann——Roch theorem using adèles (after André Weil) and give some basic examples and results from the theory of algebraic curves.