Sam Mundy

3rd year graduate student at Columbia University. My advisor is Eric Urban.



Hida Theory Seminar

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.
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."

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 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

Past Seminars

Shimura Varieties Reading Group Summer 2017
Algebraic Number Theory Meetings Spring 2016



Some papers

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.



Some things I am thinking about

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.)



Here is a diagrammatic "statement" of the weight 2 Eichler-Shimura Theorem. I have this printed on a coffee mug.

Tiny version:


Sam's email address is: sam@mundy.net