Purpose of the school
The connection between random matrix theory and the zeros of the Riemann zeta function was first suggested by Montgomery and Dyson in 1973, and later used in the 1980s to elucidate periodic orbit calculations in the field of quantum chaos. Just in the past few years it has also been employed to suggest brand new ways for predicting the behaviour of the Riemann zeta function and other L-functions. Notwithstanding these successes there has always been the problem that very few researchers are well-versed both in number theory and methods in mathematical physics. The aim of this school is to provide a grounding in both the relevant aspects of number theory, and the techniques of random matrix theory, as well as to inform the students of what progress has been made when these two apparently disparate subjects meet.
Lecturers
Estelle Basor, Michael Berry, Eugene Bogomolny, Oriol Bohigas, Brian Conrey, Dan Goldston, David Farmer, Peter Forrester, Yan Fyodorov, Roger Heath-Brown, Shinobu Hikami, Chris Hughes, Jonathan Keating, Philippe Michel, Michael Rubinstein
Topics to be covered
- ensembles of Hermitian matrices
- random matrix eigenvalue statistics
- orthogonal polynomials
- Painlevé theory and random matrix averages
- Fisher-Hartwig conjecture and Toeplitz determinants
- random matrix characteristic polynomials as models for L-functions
- universality of random matrix ensembles
- elementary number theory
- the Riemann zeta function and Dirichlet L-functions
- elliptic curves, automorphic forms and associated L-functions
- computation of L-functions
- Montgomery's conjecture on the two-point statistics of the Riemann zeta function
- Selberg's theorem on the distribution of values of the logarithm of the Riemann zeta function
- calculating moments of L-functions
- recent work utilising random matrix theory in number theory
Schedule
Lectures will begin in the morning of Monday March 29. The school will end at lunchtime on April 8.
Location and Cost
The school will take place at the Newton Institute and accommodation for participants will be provided in single study bedrooms with shared bathroom at Wolfson Court. The package cost for the school is £670. This includes accommodation, breakfast, lunch and dinner from dinner on Sunday 28 March 2004 until lunch on Thursday 8 April, 2004. Lunches, however, will only be provided during the days that lectures take place. Participants are expected to arrive on the afternoon of Sunday 28 March and depart on the afternoon of Thursday 8 April, 2004. Accommodation for extra nights may be arranged at extra cost.
Applications Forms
The closing date for the receipt of applications has now passed
Supported Participants
Some support is available for participants in this meeting from the Quantum Chaos Network and the Mathematical and Theoretical Physics group of the IOP. Please indicate your affiliations with these bodies on the application form. In addition, support for younger UK researchers is available under the Newton Institute Junior Membership scheme and NSF funding for ten graduate students enrolled in American Institutions is available through the American Institute of Mathematics.
Closing Date
The closing date for the receipt of applications is 28 November 2003
Co-sponsored by: Mathematical and Theoretical Physics group of the IOP and the National Science Foundation |
Random Matrix Approaches in Number Theory | Workshops | Newton Institute Home Page