Number theory learning seminar 2013-2014

The seminar will meet Wednesdays 2--4pm in Room 383-N . This year's seminar will focus on the Jacquet--Langlands correspondence. In the fall we will discuss representation theory in local and global aspects (and its relation with classical settings), in the winter we will discuss the trace formula and prove the Jacquet--Langlands correspondence, and in the spring we will discuss some applications to Galois representations.

For more details on what each lecture will cover with references see here .

Here are some references which may be relevant for this year's seminar:
(B) The Jacquet--Langlands correspondence, by Badulescu
(BH) The local Langlands correspondence for GL(2), by Bushnell-Henniart
(BZ) Induced representations of reductive p-adic groups. I by Bernstein-Zelevnisky
(C) Nombre de points des varietes de Shimura sur un corps fini (d'apres R. Kottwitz) by Clozel
(D) Introductory notes on p-adic group representations by DeBacker
(GJ) Forms on GL(2) from the analytic point of view by Gelbart--Jacquet, pp. 213--251 in Corvallis Proceedings
(K1) Introduction to the Langlands Program by Knapp
(K2) Representation theory of semisimple Lie groups: an overview based on examples, by Knapp
(LW) On the computation of local components of a newform by Loeffler--Weinstein

The speaking slots below are tentative, not set in stone: please contact Brian or Akshay and express your desire to speak.

Notes -- use at your own risk.

These are informal notes written by each speaker. They may change from time to time as we edit them.

Fall quarter
1 Oct. 16 Akshay Introduction to automorphic representations .pdf
2 Oct. 23 Brian C. Hecke algebras for p-adic groups .pdf
3 Oct. 30, Nov. 6 Iurie Principal series and Jacquet functors .pdf
4 Nov. 13 Macky Spherical representations and Satake isomorphism .pdf
5 Nov. 20 Niccolo Supercuspidal representations .pdf
6 Dec. 4 Zhiwei Introduction to real group representations .pdf
7, 8 Dec. 11 Akshay Discrete series and Langlands classification .pdf
Winter quarter
9 Jan. 15 Zeb Return to classical cases
10 Jan. 22 Akshay Classical and automorphic Eisenstein series I
11 Jan. 29 Akshay Classical and automorphic Eisenstein series II
12 Feb. 5, 12 Jeremy Trace formula for compact quotients I, II .pdf
13 Feb. 19 Scholze No meeting: perfectoid workshop at MSRI
14, 15 2/26, 3/5 Iurie Trace formula for non-compact quotients I, II .pdf
16 March 12 Brian C. Hecke trace via l-adic Lefschetz trace formula .pdf .pdf (stray last page)
Spring quarter
17 April 2 Brian L., Hilaf Honda--Tate I .pdf
18 April 9 Brian L., Hilaf Honda--Tate II .pdf
19 April 16 Dan L. Local-global compatibility for GL(2) .pdf
20 April 23 Zhiwei Jacquet--Langlands correspondence ([GJ], section 8) .pdf
21 April 30 Akshay The ``big picture'' on the trace formula
22 May 7 Macky Simpler form of the trace formula .pdf
23-24 May 14, 21 Zeb, Evan Hecke traces and class numbers I, II .pdf
25 May 28 Akshay Concluding remarks