About The goal of this graduate seminar is to lay the groundwork for an understanding of algebraic geometry by studying Riemann surfaces and algebraic curves.

The seminar is being organized by Matt Grimes and Professor Casalaina-Martin.

Textbook We will be working out of Algebraic Curves and Riemann Surfaces, Miranda, R., 1995.

Schedule Tuesdays at 1:00pm in MATH 350

Contact Inquiries may be directed to Matt Grimes: matthew.grimes [at] colorado.edu, or Professor Casalaina-Martin: casa [at] math.colorado.edu.
Speaker List
Bryce, Steve, Kris, Bill, David, John, Matt
August 30th
Chapter 1 An introduction to the definition and basic examples of a Riemann surface.
Presenter: Matt Grimes

We will examine the basic notions and definitions of Riemann surfaces, and explore examples. Key ideas covered will be the complex projective line and projective curves.
September 6th
Chapter 2 Functions and maps
Presenter: Steve Limburg

We will examine functions from Riemann surfaces to the complex plane and maps between Riemann surfaces. Of particular interest will be holomorphic and meromorphic functions and their properties.
September 13th
Chapter 2 Examples of Riemann surfaces
Presenter: Erica Shannon

September 20th
Chapter 2 Examples of Riemann surfaces, Part 2
Presenter: Erica Shannon

October 18th
Chapter 6 Riemann-Roch
Presenter: Mike Martinez

October 25th
Chapter 7 Applications of Riemann-Roch
Presenter: Kris Havasi

November 1st
Chapter 8 Abel's Theorem
Presenter: Matt Grimes

November 8th
Chapter 9 Sheaves and Cech Cohomology
Presenter: David Wayne

November 15th
Chapter 10 Algebraic Sheaves
Presenter: John Hower

November 29th
Chapter 11 Invertible Sheaves, Line Bundles, and H^1
Presenter: Matt Grimes