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.
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.
Lectures 4-7 by Pak-Hin Lee used Hida's blue book, "Elementary Theory of L-functions and Eisenstein Series."
He also used the notes of Banerjee-Ghate-Kumar, "\Lambda-adic Forms and the Iwasawa Main Conjecture."
Lecture 8 (the first one on the proof of the main conjecture) used Fitting ideals. A nice reference containing all of the facts I used is Nuccio's notes "Fitting Ideals."
|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||No Talk: IAS Workshop|
|November 16||Rescheduled (see below)|
|November 20||Higher Hida Theory I (5:00 in room 528)||Dave Hansen|
|November 23||No Talk: Thanksgiving|
|November 30||Higher Hida Theory II||Dave Hansen|
|December 7||Higher Hida Theory III||Dave Hansen|
|December 14||No Talk: EPFL Conference|
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.)