This is a learning seminar organized by Tom Oldfield
(toldfield@math.utexas.edu). You can find here
some electronic notes, taken during the seminar by Arun Debray.
We'll meet twice a week, and talks should aim to be an hour long.
The room will be available for a second hour if speakers wish to
use the additional time, to provide more detailed proofs,
examples, or material from starred sections that time would
otherwise not allow for.
This aim of this seminar is to get a good understanding of the
tools required to understand and undertake modern algebraic
geometry. We'll cover the material in Ravi Vakil's
online textbook, "The Rising Sea", at a rate of around one chapter
a week. Working through Vakil's notes makes it very easy to write
talks, since the notes themselves are very discursive and provide
a lot of intuition. However, the notes include relatively few
proofs so speakers should attempt to provide proofs in as much
detail as time allows for.
The technical details of algebraic geometry are notoriously difficult, so those who want to get a firm understanding of the details should aim to do at least some of the exercises from the relevant material outside of the seminar each week. Those who just want to get an overall picture of the field and a flavour for the kinds of problems it tackles are of course more than welcome to simply attend the talks.
The schedule of talks is as follows:
Week Beginning | Topic | Speakers |
---|---|---|
16th May |
Chapter 10 - "Seperated and proper morphisms and,
(finally!) varieties" |
Tom Oldfield, Arun Debray |
23rd May |
Chapter 11 - "Dimension" |
Gill Grindstaff, Richard Wong |
30th May |
Chapter 12 - "Regularity and smoothness" |
Jay Hathaway, Daniel Chupin |
6th June |
Chapter 13 - "Quasicoherent and coherent sheaves" |
Yan Zhou, Yuri Sulyma |
13th June |
Chapter 14 - "Line bundles - Invertible sheaves and
divisors" |
Arun Debray, Tom Oldfield |
20th June |
Chapter 15 - "Quasicoherent sheaves on projective
A-schemes" |
Daniel Chupin, Richard Wong |
27th June | Chapter 16 - "Pushforwards and pullbacks of
quasicoherent sheaves" |
Gill Grindstaff, Jay Hathaway |
4th July |
Appendix A - "Truths that we hold to be self-evident" |
John Adams, Thomas Jefferson |
11th July | Chapter 17 - "Relative versions of Spec and Proj, and projective morphisms" | Yan Zhou, Arun Debray |
18th July | Chapter 18 - "Cech cohomology of quasicoherent sheaves" |
Yuri Sulyma, Daniel Chupin |
25th July | Chapter 19 - "Application: Curves" | Tom Oldfield, Arun Debray |
22nd August |
That's all, folks! |