Zeév Rudnick (Tel Aviv University)

Conférences dans le cadre de l'atelier sur la Statistique et théorie des nombres
(15-19 septembre 2014)
Lectures at the Workshop on Statistics and Number Theory (September 15-19, 2014)

La première conférence sera donnée en deux parties.
The first lecture will be given in two parts.

Première partie / Part 1
Mardi 16 septembre 2014, 09h30 / Tuesday, September 16, 2014, 9:30 am

Seconde partie / Part 2
Mercredi 17 septembre 2014, 15h30 / Wednesday, September 17, 2014, 3:30 pm

Analytic number theory for polynomials over a finite field, random permutations, and matrix integrals

Résumé/Abstract : In these lectures I will explore traditional problems of analytic number theory in the context of function fields over a finite field. Several such problems which are currently viewed as intractable over the integers, have recently been addressed in the function field context with vastly different tools than those of traditional analytic number theory, and the resulting theorems can be used to check existing conjectures over the integers, and to generate new ones. Among the topics discussed will be some squarefree values of polynomials, the Mobius randomness principle, and statistics of primes and of squarefrees.

Centre de recherches mathématiques
Pavillon André-Aisenstadt, Université de Montréal
Salle / Room 6214

Jeudi 18 septembre 2014, 16h00 / Thursday, September 18, 2014, 4:00 pm

Sums of three squares and spatial statistics on the sphere

Résumé/Abstract: A celebrated result of Legendre and Gauss determines which integers can be represented as a sum of three squares, and for those it is typically the case that there are many ways of doing so.  These different representations give collections of points on the unit sphere, and a fundamental result, conjectured by Linnik, is that under a simple condition these become uniformly distributed on the sphere. In the lecture I explore what happens beyond uniform distribution, giving evidence to randomness on smaller scales.  This is in sharp contrast to what happens with sums of two or four or more squares. (joint work with J. Bourgain and P. Sarnak).

Centre de recherches mathématiques
Pavillon André-Aisenstadt, Université de Montréal
Salle / Room 1140

Une réception suivra la conférence au Salon Maurice-L'Abbé, Pavillon André-Aisenstadt (Salle 6245).
A reception will follow at the Salon Maurice-L'Abbé, Pavillon André-Aisenstadt (Room 6245).