École d'été 2014 Théorie analytique des nombres

9 juil. 2014, 09:00 → 23 juil. 2014, 18:00 Europe/Paris

Centre de conférences Marilyn et James Simons (IHES)

Objective

­ ­ Organised as part of the "IHÉS Lectures", this Summer School aims to train PhD students, post-docs and young researchers on recent topics of Analytic Number Theory and to promote exchanges between young researchers of all nationalities.

Analytic number theory began with the first questions concerning the distribution of prime numbers. Since then, the subject has evolved in many directions; it has influenced and interacted with many areas of mathematics, by lending or borrowing ideas going from combinatorics to representation theory, and from modular forms to the deepest reaches of algebraic geometry.

The summer school will cover both classical and emerging topics of analytic number theory, with a focus on the properties of prime numbers:

(1) advanced sieve methods and their refinements, including approaches to gaps between primes and asymptotic sieve for primes;

(2) distribution of arithmetic functions in arithmetic progressions, especially in ranges beyond the direct reach of the Riemann Hypothesis;

(3) exponential sums over finite fields, and their analytic applications, with a focus on the formalism and uses of Frobenius trace functions;

(4) modular forms and associated L-functions, and other analytic aspects of the Langlands program, such as the behavior of torsion homology;

(5) additive combinatorics.

 

­ ­

Avec le soutien de
la Société Générale

 

Speakers

• Jean BOURGAIN (Princeton, USA)
• Valentin BLOMER (Universität Göttingen, Germany)
• Etienne FOUVRY (Université Paris-Sud, Orsay)
• Andrew GRANVILLE (Université de Montréal, Québec)
• Harald HELFGOTT (ENS, Paris)
• Henryk IWANIEC (Rutgers University, Piscataway, USA)
• Emmanuel KOWALSKI (ETH Zürich, Switzerland)
• Philippe MICHEL (EPFL Lausanne, Switzerland)
• Peter SARNAK (IAS Princeton, USA)
• Kannan SOUNDARARAJAN (Stanford University, USA)
• Terence TAO (UCLA, USA)
• Akshay VENKATESH (Stanford University, USA)

Autre événement

Workshop on Analytic Number Theory and Geometry
organisé par Farrell Brumley
24-25 juillet, 2014
Université Paris 13

Local map acces plan_ecole_ete2014.pdf

Poster Poster Ecole d'ete 2014

Programme PROGRAMMEAngl.pdf

Where can I eat in the area PlacesToEat.pdf

mercredi 9 juillet

09:00 → 10:00 Welcome coffee

10:00 → 11:00 J. Bourgain

The orbital circle method and applications / Toral eigenfuctions and their nodal sets (1/2)

11:00 → 11:30 Break

11:30 → 12:30 T.Tao

Boundeg gaps between primes (1/3)

12:30 → 14:30 Lunch

14:30 → 15:30 K. Soundararajan

L-functions (1/4)

15:30 → 16:00 Break

16:00 → 17:00 A. Granville

The pretentious approach to analytic number theory (1/3)

jeudi 10 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 J. Bourgain

The orbital circle method and applications / Toral eigenfuctions and their nodal sets (2/2)

10:30 → 11:00 Break

11:00 → 12:00 K. Soundararajan

L-functions (2/4)

12:00 → 14:30 Buffet-lunch at IHES

14:30 → 15:30 K. Soundararajan

L-functions (3/4)

15:30 → 16:00 Break

16:00 → 17:00 A. Granville

The pretentious approach to analytic number theory (2/3)

vendredi 11 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 T. Tao

Boundeg gaps between primes (2/3)

10:30 → 11:00 Break

11:00 → 12:00 H. Iwaniec

Sifting for primes (1/3)

12:00 → 14:30 Lunch

14:30 → 15:30 K. Soundararajan

L-functions (4/4)

15:30 → 16:00 Coffee break

16:00 → 17:00 A. Granville

The pretentious approach to analytic number theory (3/3)

samedi 12 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 T. Tao

Boundeg gaps between primes (3/3)

10:30 → 11:00 Break

11:00 → 12:00 H. Iwaniec

Sifting for primes (2/3)

mardi 15 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 Ph. Michel

Automorphic forms for GL(2) (1/4)

10:30 → 11:00 Break

11:00 → 12:00 H. Iwaniec

Sifting for primes (3/3)

12:00 → 14:30 Lunch

14:30 → 15:30 A. Venkatesh

Analytic number theory around torsion homology (1/4)

15:30 → 16:30 Break

16:30 → 17:30 E. Fouvry

Analytic aspects of Cohen-Lenstra heuristics (1/4)

mercredi 16 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 Ph. Michel

Automorphic forms for GL(2) (2/4)

10:30 → 11:00 Break

11:00 → 12:00 H. Helfgott

Growth in groups and applications (1/4)

12:00 → 14:30 Lunch

14:30 → 15:30 A. Venkatesh

Analytic number theory around torsion homology (2/4)

15:30 → 16:00 Break

16:00 → 17:00 E. Fouvry

Analytic aspects of Cohen-Lenstra heuristics (2/4)

jeudi 17 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 V. Blomer

Automorphic forms in higher rank (1/4)

10:30 → 11:00 Break

11:00 → 12:00 H. Helfgott

Growth in groups and applications (2/4)

12:00 → 14:30 Buffet-lunch at IHÉS

14:30 → 15:30 E. Kowalski

Trace functions over finite fields (1/4)

15:30 → 16:00 Break

16:00 → 17:00 Ph. Michel

Automorphic forms for GL(2) (2/3)

vendredi 18 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 V. Blomer

Automorphic forms in higher rank (2/4)

10:30 → 11:00 Break

11:00 → 12:00 A. Venkatesh

Analytic number theory around torsion homology (3/4)

12:00 → 14:30 Lunch

14:30 → 15:30 E. Fouvry

Analytic aspects of Cohen-Lenstra heuristics (3/4)

15:30 → 16:00 Break

16:00 → 17:00 E. Kowalski

Trace functions over finite fields (2/4)

lundi 21 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 Ph. Michel

Automorphic forms for GL(2) (4/4)

10:30 → 11:00 Break

11:00 → 12:00 H. Helfgott

Growth in groups and applications (3/4)

12:00 → 14:30 Lunch

14:30 → 15:30 A. Venkatesh

Analytic number theory around torsion homology (4/4)

15:30 → 16:00 Break

16:00 → 17:00 V. Blomer

Automorphic forms in higher rank (3/4)

mardi 22 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 E. Fouvry

10:30 → 11:00 Break

11:00 → 12:00 E. Kowalski

Trace functions over finite fields (3/4)

12:00 → 14:30 Lunch

14:30 → 15:30 V. Blomer

Automorphic forms in higher rank (4/4)

mercredi 23 juillet

09:00 → 09:30 Welcome coffee

09:30 → 10:30 H. Helfgott

Growth in groups and applications (4/4)

10:30 → 11:00 Break

11:00 → 12:00 E. Kowalski

Trace functions over finite fields (4/4)