3rd year graduate student at Columbia University. My advisor is Eric Urban.
This semester Dave Hansen and I are organizing a seminar on Hida Theory.
Time and place: Thursdays 1:00-2:15 in Mathematics 622.
Here are notes, taken by Pak-Hin Lee.
References:
Lecture 1 was based off Chapter 2 of Christopher Skinner's CMI notes, "Galois Representations, Iwasawa Theory, and Special Values of L-functions."
Lecture 2 contains material that can be found, for instance, in Lang's "Cyclotomic Fields I and II." See Chapter 5.
Tentative Schedule:
Date | Title | Speaker |
---|---|---|
September 7 | Ribet's Converse to Herbrand's Theorem | Sam Mundy |
September 14 | Basic Iwasawa Theory | Sam Mundy |
September 21 | p-Adic Properties of L-Functions | Sam Mundy |
September 28 | \Lambda-adic Modular Forms | Pak-Hin Lee |
October 5 | Ordinary \Lambda-adic Forms | Pak-Hin Lee |
October 12 | Hida Theory and \Lambda-adic Galois Representations | Pak-Hin Lee |
October 19 | \Lambda-adic Representations via Pseudo-representations | Pak-Hin Lee |
October 26 | Proof of the Main Conjecture for Q, I | Sam Mundy |
November 2 | Proof of the Main Conjecture for Q, II | Sam Mundy |
November 9 | ||
November 16 | ||
November 23 | No talk: Thanksgiving | |
November 30 | ||
December 7 | ||
December 14 |
Shimura Varieties Reading Group Summer 2017
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.)