2nd year graduate student at Columbia University.
I am interested in arithmetic geometry and related areas.
This summer we will meet weekly to discuss Shimura varieties.
Our main reference is
[Milne] Milne's notes on Shimura Varieties.
There are also some errata and Poonen's extensive list of comments.
[Lan] Kai-Wen Lan's notes.
[Youcis] Alex Youcis has a blog post on motivation for the theory of Shimura varieties.
Times and dates:
We will meet (approximately) weekly in room 307 in the math building at 4:00 on Fridays. We have the room reserved until 6:00 (though I don't necessarily expect discussions to last for two whole hours) and until September 1st (similar comment here.)
There will not necessarily be any talks. Rather, we will read on our own and discuss the reading in front of the blackboard.
We should bring questions, comments, and ideas about, and supplementary to, the reading material. If you feel like you might have trouble contributing during the sessions, try adapting the this advice about seminars to reading instead.
507 307, we have access to a good okay blackboard, and we should use it as much as is reasonable. We should write our questions on the blackboard before trying to answer them, for example.
If you have any ideas or comments about anything from references to logistics, feel free to email me.
The following table contains the dates we met/will meet, along with references to the reading that we discussed/will discuss.
|May 12||[Milne] Chapter 1|
|May 19||[Milne] Chapter 2|
|May 26||[Milne] Chapter 3|
|June 2||[Milne] Chapter 4|
|June 9||[Milne] Chapter 5, up to page 56|
|June 16||[Milne] Rest of chapter 5|
|June 23||[Lan] Chapters 1-3|
Algebraic Number Theory Meetings Spring 2016
Here is my senior thesis (45 pages). The last section contains a new adelic proof of the Riemann-Roch Theorem for number fields.
Here is a link to my paper on this proof on the arXiv (8 pages).
Local Compactness and Number Theory: These are the notes for a seminar course (Math 639 Section 001) which I taught at UNM in the spring of 2015.
Using compact or discrete rings to extend their Pontrjagin duals, in the category of locally compact abelian groups.
Example: One can extend the circle by the integers to obtain the reals (I have a weird way of doing this.)
Adelic surface area (see my undergraduate thesis.)