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

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

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

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

  4. 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.

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

  6. 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.

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

  8. Amnon Ta-Shma will talk about something not from the book, yet, related to the topic of the seminar

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

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

  11. 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 10:00-12:00 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 1-6.