##### 8/17/2011

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

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.

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.

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.

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

Presenter: Erica Shannon

##### September 20th

Chapter 2
Examples of Riemann surfaces, Part 2

Presenter: Erica Shannon

Presenter: Erica Shannon

##### October 18th

Chapter 6
Riemann-Roch

Presenter: Mike Martinez

Presenter: Mike Martinez

##### October 25th

Chapter 7
Applications of Riemann-Roch

Presenter: Kris Havasi

Presenter: Kris Havasi

##### November 1st

Chapter 8
Abel's Theorem

Presenter: Matt Grimes

Presenter: Matt Grimes

##### November 8th

Chapter 9
Sheaves and Cech Cohomology

Presenter: David Wayne

Presenter: David Wayne

##### November 15th

Chapter 10
Algebraic Sheaves

Presenter: John Hower

Presenter: John Hower

##### November 29th

Chapter 11
Invertible Sheaves, Line Bundles, and H^1

Presenter: Matt Grimes

Presenter: Matt Grimes