School on NT and RMT (almost final version)

The instructors for the School are:
Brian Conrey, David Farmer, Steve Gonek, Chris Hughes, Jon Keating,
Francesco Mezzadri, Mike Rubinstein, Nina Snaith, Doug Ulmer, and Matt Young.

	Tuesday, May 30	Wednesday, May 31	Thursday, June 1	Friday, June 2	Saturday, June 3
9:00	Overview Farmer	Modular forms 1: Basics, Hecke operators Farmer	Modular forms 2: Peterson formula, Selberg trace formula Farmer	Catch up: make sure nobody is lost TBA	Function field 1: basics Ulmer
10:15	RMT1: The big picture. Applications to physics and the real world Keating	RMT 3: Toeplitz, Szego, Heine, etc Mezzadri	RMT 6: General probability, connection between moments and distribution Hughes	Modular forms 3: Maass forms, GL(3) and other groups Farmer	RMT 10: Orthogonal polynomial methods Mezzadri
11:30	Basic zeta 1: zeta, Dirichlet L, EP, FE, Hadamard, Phragmen-Lindelof Farmer	RMT 4: Pair correlation (full details), n-level density, determinant kernel Keating	Moments 3: Applications to zero density etc., mollification and amplification Gonek	RMT 8: Nearest neighbour spacing via: correlations Fredholm determinant Painleve Snaith	Modular forms 4: Kloosterman sums, Kuznetsov Young
Lunch
2:00	RMT2: Classical compact groups, Weyl integration formula, Haar measure Hughes	RMT 5: Distribution of the log char poly, moments via Selberg (unitary and maybe symplectic) Snaith	RMT data: how to generate random matrices and do experiments Mezzadri	Moments 4: Families in general, The recipe Young	Function field 2: compute a monodromy group Ulmer
3:15	Basic zeta 2: zeros, N(T), S(T), Montgomery, some pictures Rubinstein	Moments 2: GL(1) continued What is known, general form of conjectures (leading term only) Gonek	Elliptic curves: basic properties and terminology conductor, discriminant how to compute rank, torsion group, regulator, etc modularity Young	RMT 9: Densities and correlations, comparison between different groups Snaith	Classifying a family: moments and one-level density Conrey
4:30	Moments 1: GL(1) examples T and q aspects Conrey	RMT/NT: Some details on the connection between NT and RMT Hughes	RMT 7: Moments for orthogonal group, distribution and connection to elliptic curves Keating	L-functions: Converse theorems, Selberg class Conrey	How to do L-function numerics Rubinstein

There are (so far) three talks at the conference which can be considered as direct continuations of the school:
Brian Conrey will talk about Applications of the Ratios Conjecture
Matt Young will lecture on "Life beyond the diagonal"
Dan Bump will explain his work with Alex Gamburd on Ratios of characteristic polynomials.

Students should purchase the proceedings of the Newton School on Number Theory and Random Matrix Theory. There will be assigned reading and homework before the Rochester school. The book is available from Amazon or Barnes & Noble.

Homework will be assigned during the school, and there will be a place for students to gather in the evenings.

For more information email     ntrmt (at) aimath.org