Seminar on Algebraic Curves and Riemann Surfaces
Winter 2019/20
Syllabus
Towards having a better understanding of Algebraic Geometric Codes, in this seminar we will study the foundations of algebraic curves and Riemann Surfaces (which takes place over the complex field).
Lectures

Noam Peri on the basic definitions of complex charts, complex structures, and Riemann Surfaces, following Chapter 1.1.

Shir Peleg will present first examples of Riemann Surfaces and projective curves following Chapters 1.2 and 1.3.

Libi Lubovich will discuss functions on Riemann Surfaces and examples of meromorphic functions following Chapters 2.1 and 2.2.

Ori Sberlo will talk about holomorphic maps between Riemann Surfaces and their global properties following Chapters 2.3 and 2.4, excluding Hurwitz's genus formula.

Noam Peri will cover some notions from topology that we need for proceeding further, in particular, orientable surfaces and their genus.

Shir Peleg will talk about Hurwitz's genus formula following Chapter 2.4 and discuss more elementary examples of Riemann surfaces following Chapter 3.1.

Libi Lubovich will talk and some less elementary examples, following Chapter 3.2.

Amnon TaShma will talk about something not from the book, yet, related to the topic of the seminar

Noam Peri talked about group actions an Riemann Surfaces following Chapter 3.3

Noam continued to discuss Hurwtiz's theorem and presented an introductory to the fundamental group and to covering spaces.

I (Gil) gave a somewhat slower introduction to the basic notions from algebraic topology that we need. To be continued next time.

Prerequisite
Group theory, complex analysis, and topology.
When and where
The lectures take place on Monday 10:0012:00 at Check Point 280.
Reading material
The seminar is based on Rick Miranda's fantastic book Algebraic Curves and Riemann Surfaces. The goal is to cover Chapters 16.