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.

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 |

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.)

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