School on NT and RMT

This is the schedule for the School on Number Theory and Random Matrix Theory, held at the University of Rochester, Rochester, NY, USA from May 30 to June 3, 2006.

The hyperlinks take you to the scanned copies of the lecture notes.

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

(Names in parentheses) are the note-takers for chalk talks.

Tuesday, May 30 Wednesday, May 31 Thursday, June 1 Friday, June 2 Saturday, June 3

9:00 Number theory background I
David Farmer Modular forms and L-functions
David Farmer Modular forms II
Mike Rubinstein Catch-up session:
Farmer 1
Conrey (Brian Winn)
Farmer 2 Function fields: Basics
Doug Ulmer

10:15 The big picture: Applications to physics and the real world (Shahed Sharif)
Jon Keating Asymptotics of averages over the classical compact groups
Francesco Mezzadri Things you need to know from probability theory
Chris Hughes Maass forms, the geometry of Gamma_0(N), L-functions, quantum chaos, ...
David Farmer Orthogonal polynomials techniques
Francesco Mezzadri

11:30 Number theory background II
David Farmer Two-point correlation function (Brian Winn)
Jon Keating Moments III
Steve Gonek Nearest Neighbour Spacing
Nina Snaith Detailed moments conjectures
Mike Rubinstein

Lunch

2:00 Haar measure and Weyl integration
Chris Hughes Mean values of characteristic polynomials
Nina Snaith Numerical experiments and random matrices
Francesco Mezzadri Families of L-functions
Matt Young Function fields: Monodromy groups
Doug Ulmer

3:15 Primes and zeros
Mike Rubinstein Moments II
Steve Gonek Basics of elliptic curves
Matt Young Densities and correlations
Nina Snaith Random matrix shifted moments (Brian Winn)
Brian Conrey

4:30 Moments I (Brian Winn)
Brian Conrey Connections between L-functions and random matrix theory: Zeros and moments
Chris Hughes Moments for orthogonal group and ranks of elliptic curves (Brian Winn)
Jon Keating The Selberg class and higher degree L-functions (Brian Winn)
Brian Conrey How to do L-function numerics
Mike Rubinstein

For more information email ntrmt (at) aimath.org

	Tuesday, May 30	Wednesday, May 31	Thursday, June 1	Friday, June 2	Saturday, June 3
9:00	Number theory background I David Farmer	Modular forms and L-functions David Farmer	Modular forms II Mike Rubinstein	Catch-up session: Farmer 1 Conrey (Brian Winn) Farmer 2	Function fields: Basics Doug Ulmer
10:15	The big picture: Applications to physics and the real world (Shahed Sharif) Jon Keating	Asymptotics of averages over the classical compact groups Francesco Mezzadri	Things you need to know from probability theory Chris Hughes	Maass forms, the geometry of Gamma_0(N), L-functions, quantum chaos, ... David Farmer	Orthogonal polynomials techniques Francesco Mezzadri
11:30	Number theory background II David Farmer	Two-point correlation function (Brian Winn) Jon Keating	Moments III Steve Gonek	Nearest Neighbour Spacing Nina Snaith	Detailed moments conjectures Mike Rubinstein
Lunch
2:00	Haar measure and Weyl integration Chris Hughes	Mean values of characteristic polynomials Nina Snaith	Numerical experiments and random matrices Francesco Mezzadri	Families of L-functions Matt Young	Function fields: Monodromy groups Doug Ulmer
3:15	Primes and zeros Mike Rubinstein	Moments II Steve Gonek	Basics of elliptic curves Matt Young	Densities and correlations Nina Snaith	Random matrix shifted moments (Brian Winn) Brian Conrey
4:30	Moments I (Brian Winn) Brian Conrey	Connections between L-functions and random matrix theory: Zeros and moments Chris Hughes	Moments for orthogonal group and ranks of elliptic curves (Brian Winn) Jon Keating	The Selberg class and higher degree L-functions (Brian Winn) Brian Conrey	How to do L-function numerics Mike Rubinstein