Workshop on Recent Trends in Analytic Number Theory

Clay Mathematics Institute/Institute for Advanced Study

April 12, 2000 - April 15, 2000

Location Seminar Room
Mathematics Building
Institute for Advanced Study
Olden Lane
Princeton, New Jersey
Enrico Bombieri and Henryk Iwaniec
  This workshop is being held in partnership with the Clay Mathematics Institute.
Jean Bourgain - Institute for Advanced Study
Fernando Chamizo - Universidad Autonoma de Madrid
William Duke - Rutgers University
John Friedlander - IAS/University of Toronto
Andrew Granville - University of Georgia
David Heath-Brown, Oxford University
Dennis Hejhal - IAS/Uppsala University/University of Minnesota
Jerzy Kaczorowski - Collegium im. Adama Mickiewicza
Philippe Michel - IAS/Universite Montpellier II
Yoichi Motohashi - Nihon University
Ken Ono - Penn State University
Alberto Perelli - IAS/University of Genova, Italy
Fernando Rodriguez-Villegas - University of Texas at Austin
Peter Sarnak - IAS/Princeton University
Joseph Silverman - Brown University
Kannan Soundararajan - IAS/American Institute of Mathematics
Agenda Wednesday, April 12

10 am - 11 Peter Sarnak, IAS/Princeton University
"L-Functions and Equidistribution"

11:10 - 12:10 Philippe Michel, IAS/Université Montpellier II, FranceÂ
"Rankin-Selberg L Functions in the Level Aspect"

12:10 - 2 LUNCH, Institute Dining Hall

2 - 3 Kannan Soundararajan, IAS/Princeton University
"Real Zeros of Quadratic Dirichlet L-Functions."

3 - 3:30 REFRESHMENT BREAK, Fuld Hall Common Room

3:30 - 4:30 Jean Bourgain, Institute for Advanced Study
"On Large Values Estimates for Dirichlet Sums and the
Density Hypothesis for the Zeta Function."

Thursday, April 13

11:10 - 12:10 William Duke, Rutgers University
"The Splitting of Primes in Division Fields of Elliptic Curves."

12:10 - 2 LUNCH, Institute Dining Hall

2 - 3 Fernando Rodriguez-Villegas, University of Texas - Austin
"Distributuion of Sha of Twists"

3 - 3:30 REFRESHMENT BREAK, Fuld Hall Common Room

3:30 - 4:30 Ken Ono, Penn State University
"Tate-Shafarevich Groups and Ranks of Quadratic Twists of
Elliptic Curves."

4:30 - 5:30 Joseph Silverman, Brown University
"Canonical Heights on Elliptic Curves: An Analytic Perspective."

Friday, April 14

10 am - 11 Andrew Granville, University of Georgia

11:10 - 12:10& D. Roger Heath-Brown, Oxford University
"Counting Rational Points on Curves and Surfaces."

12:10 - 2 LUNCH, Institute Dining Hall

2 - 3 Dennis Hejhal, IAS/Uppsala Univ./Univ. of Minnesota.

3 - 3:30 REFRESHMENT BREAK, Fuld Hall Common Room

3:30 - 4:30
"Explicit Formulas for Mean Values of a Class of Zeta-Functions."

4:30 - 5:30 Fernando Chamizo, Universidad Autonoma de Madrid
"The Hyperbolic Circle Problem and its Applications."

Saturday, April 15

10 am - 11
"On Degree Conjecture in the Selberg Class."

11:10 - 12:10 Alberto Perelli, IAS/University of Genova, Italy
"The Selberg Class: Invariants and Rigidity."

12:10 - LUNCH, Institute Dining Hall
Workshop concludes


This year, 1999 - 2000, the School of Mathematics of the Institute for Advanced Study is having a special program on automorphic forms and L-functions with emphasis on analytic methods. Moreover, other aspects of classical and modern number theory, such as equidistribution, exponential and character sums over varieties and elliptic curves have also been part of our focus.

Stimulated by the currect activity and in partnership with the Clay Mathematics Institute, we are going to conclude the program with a workshop on Recent Trends in Analytic Number Theory to be held at the Insitute during April 12 - 15, 2000.

The main objective of this workshop will be to present the best (old and new) achievements in the described subjects, as well as to expand interactions between various specialists.



Date & Time

April 15, 2000 | 12:00am – April 20, 2000 | 12:00am