Number Theory

January 11 - April 30, 2021

This program focuses on three connected areas of number theory: Analytic Number Theory, Number Theory and Probability, as well as Rational Points. The aim is to bring together researchers from these areas in order to push the boundaries of current central questions, building on fascinating recent advances in the individual areas.

Analytic Number Theory has seen a number of unexpected breakthroughs on very fundamental questions during recent years. Starting with Green and Tao’s work on progressions in the primes and Goldston, Pintz and Yıldırım’s work on prime gaps, progress in our understanding of the distribution of primes included breakthrough work by Zhang, Maynard and Tao on bounded gaps between primes. Subsequent progress on large gaps between primes includes work by Ford, Green, Konyagin, Maynard and Tao, who, building on arguments by Rankin, Maier and Pomerance together with more recent results on hypergraph coverings, resolve a long standing conjecture of Erdős on the maximum gap between consecutive primes (up to x). Apart from prime number theory, multiplicative number theory has seen major progress: the development of the pretentious approach to number theory by Granville and Soundararajan, and Matomäki and Radziwill’s breakthrough on multiplicative functions in short intervals, leading to the resolution of the Erdős Discrepancy problem.

The birth of Probabilistic Number Theory is often credited to Erdős and Kac, who showed that the distribution of the number of prime factors of large random integers is essentially Gaussian. Applications of classical probabilistic techniques in number theory and the study of L-functions are now abundant but the usage of modern probability techniques has not been so common. However, this has changed recently: random matrix theory, random fragmentation processes, Poisson branching processes, Stein’s method and martingales now play a key role in advancements on new and classical problems in number theory.

The study of Rational Points on varieties is connected to one of the oldest problems in number theory, namely that of understanding integral solutions to Diophantine equations. Central questions here involve both the existence and distribution of rational points. Our understanding of such questions has been considerably pushed forward not just by advances within Diophantine geometry (obstruction theory, descent, fibration method, torsors), but also by the interplay of algebraic geometry on one side and analytic methods from number theory (circle method, additive combinatorics), harmonic analysis, and ergodic theory / dynamical systems on the other side.

 

There will be two bridging workshops during the program, with talks equally divided between the adjacent thematic sections, aiming for discovery of new connections.

 

  • Jan 11 – Feb 5: Section with focus on Number Theory and Probability
  • Feb 8 – 12: Bridging workshop
  • Feb 15 – Mar 19: Section with focus on Analytic Number Theory
  • Mar 22 – 26: Bridging workshop
  • Mar 29 – Apr 30: Section with focus on Rational Points

 

Participation in the program is by invitation only.

 

Seminars Scroll to the next upcoming seminar

  • Joint Moments January 18 17:00 - 18:00

    Joint Moments

  • The shapes of exponential sums January 25 17:00 - 18:00

    The shapes of exponential sums

  • Monday Seminar Series February 01 17:00 - 18:00

    Monday Seminar Series

  • Higher moments of primes in intervals and in arithmetic progressions, I February 08 17:00 - 17:45

    Higher moments of primes in intervals and in arithmetic progressions, I

  • Higher moments of primes in intervals and in arithmetic progressions, II February 08 18:00 - 18:45

    Higher moments of primes in intervals and in arithmetic progressions, II

  • Uniform Titchmarsh divisor problems February 10 18:15 - 19:15

    Uniform Titchmarsh divisor problems

  • Sums of two almost twin primes February 15 17:00 - 18:00

    Sums of two almost twin primes

  • Discrepancy Problems for Multiplicative Functions over F_q[t] February 17 18:15 - 19:15

    Discrepancy Problems for Multiplicative Functions over F_q[t]

  • Large fluctuations of random multiplicative functions February 22 17:00 - 18:00

    Large fluctuations of random multiplicative functions

  • The distribution of the Estermann function and other quantum modular forms March 01 17:00 - 18:00

    The distribution of the Estermann function and other quantum modular forms

  • Lattice points on hyperbolic circles March 03 18:15 - 19:15

    Lattice points on hyperbolic circles

  • Moments of Dirichlet $L$-functions March 08 17:00 - 18:00

    Moments of Dirichlet $L$-functions

  • Modular zeros in the character table of the symmetric group. March 10 18:15 - 19:15

    Modular zeros in the character table of the symmetric group.

  • Poissonian gap distributions of dilated sequences March 15 17:00 - 18:00

    Poissonian gap distributions of dilated sequences

  • Can a random lattice and its dual be independent? March 17 18:15 - 19:15

    Can a random lattice and its dual be independent?

  • Exponential sums with multiplicative coefficients and applications March 22 17:00 - 18:00

    Exponential sums with multiplicative coefficients and applications

  • Bounds on shifted convolution sums March 24 18:15 - 19:15

    Bounds on shifted convolution sums

  • Evaluating the wild Brauer group March 29 17:00 - 18:00

    Evaluating the wild Brauer group

  • Local-global principles for homogeneous spaces over some two-dimensional geometric global fields March 31 17:00 - 18:00

    Local-global principles for homogeneous spaces over some two-dimensional geometric global fields

  • Mini-conference, day 1 April 12 16:00 - 17:45

    Mini-conference, day 1

  • Mini-conference, day 2 April 14 16:00 - 17:30

    Mini-conference, day 2

  • Mini-conference, day 3 April 16 14:00 - 15:30

    Mini-conference, day 3

  • The distribution of rational points on some smooth spherical Fano varieties April 19 17:00 - 18:00

    The distribution of rational points on some smooth spherical Fano varieties

  • Some updates on thin exceptional sets in Manin’s conjecture April 21 10:30 - 11:00

    Some updates on thin exceptional sets in Manin’s conjecture

  • On The Hasse Principal for Complete Intersections April 21 11:10 - 11:40

    On The Hasse Principal for Complete Intersections

  • Distribution of the number of ramified primes in certain cyclic extensions. April 26 16:00 - 16:30

    Distribution of the number of ramified primes in certain cyclic extensions.

  • Uniform bounds and effectivity results for singular K3 surfaces April 26 16:40 - 17:10

    Uniform bounds and effectivity results for singular K3 surfaces

  • On n-torsion in class groups of number fields April 28 17:00 - 18:00

    On n-torsion in class groups of number fields

Participants

Name University Country Arrival and Departure
Ardavan
Afshar
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 11 - Apr 30, 2021
Sandro
Bettin
University: University of Genova City: Italy Arrival and Departure: Jan 11 - Feb 13, 2021
Valentin
Blomer
University: University of Bonn City: Germany Arrival and Departure: Jan 11 - Apr 30, 2021
Julia
Brandes
University: Chalmers/University of Gothenburg City: Sweden Arrival and Departure: Apr 11 - Apr 30, 2021
Martin
Bright
University: Universiteit Leiden City: The Netherlands Arrival and Departure: Mar 21 - Apr 30, 2021
Tim
Browning
University: IST Austria City: Austria Arrival and Departure: Mar 21 - Apr 30, 2021
Jörg
Brüdern
University: Universität Göttingen City: Germany Arrival and Departure: Mar 21 - Apr 30, 2021
Carlos Andrés
Chirre Chávez
University: NTNU - Norwegian University of Science and Technology City: Norway Arrival and Departure: Jan 25 - Apr 30, 2021
Sam
Chow
University: University of Warwick City: United Kingdom Arrival and Departure: Mar 15 - Apr 30, 2021
Jean-Louis
Colliot-Thélène
University: Université Paris-Sud City: France Arrival and Departure: Mar 21 - Apr 30, 2021
Régis
de la Bretèche
University: Université Paris Diderot, Paris 7 City: France Arrival and Departure: Jan 11, Feb 1 - Jan 23, Feb 13, 2021
Ulrich
Derenthal
University: University of Hannover City: Germany Arrival and Departure: Mar 15 - Apr 10, 2021
Sary
Drappeau
University: Aix-Marseille University City: France Arrival and Departure: Feb 7 - Feb 12, 2021
Alexander
Dunn
University: California Institute of Technology, Caltech City: United States Arrival and Departure: Jan 11 - Mar 19, 2021
Dennis
Eriksson
University: Chalmers/University of Gothenburg City: Sweden Arrival and Departure: Mar 29 - Apr 2, 2021
Anne-Maria
Ernvall-Hytönen
University: University of Helsinki City: Finland Arrival and Departure: Jan 11 - Jan 24, 2021
Daniel
Fiorilli
University: Université Paris-Saclay City: France Arrival and Departure: Jan 11 - Feb 13, 2021
Kevin
Ford
University: University of Illinois at Urbana-Champaign City: United States Arrival and Departure: Jan 11 - Mar 19, 2021
Christopher
Frei
University: University of Manchester City: United Kingdom Arrival and Departure: Mar 21 - Apr 30, 2021
John
Friedlander
University: University of Toronto City: Canada Arrival and Departure: Feb 27 - Mar 28, 2021
Maxim
Gerspach
University: ETH Zürich City: Switzerland Arrival and Departure: Jan 11 - Apr 30, 2021
Andrew
Granville
University: Université de Montréal City: Canada Arrival and Departure: Jan 11, Feb 15 - Feb 5, Mar 19, 2021
David
Harari
University: Université Paris-Sud City: France Arrival and Departure: Apr 6 - Apr 30, 2021
Adam
Harper
University: University of Warwick City: United Kingdom Arrival and Departure: Jan 11 - Mar 19, 2021
Roger
Heath-Brown
University: University of Oxford City: United Kingdom Arrival and Departure: Mar 21 - Apr 30, 2021
Diego
Izquierdo
University: Université Paris-Sud City: France Arrival and Departure: Mar 22 - Apr 30, 2021
Florent
Jouve
University: Université de Bordeaux City: France Arrival and Departure: Feb 14 - Mar 20, 2021
Jonathan
Keating
University: University of Oxford City: United Kingdom Arrival and Departure: Jan 31 - Feb 13, 2021
Oleksiy
Klurman
University: University of Bristol City: United Kingdom Arrival and Departure: Jan 11 - Apr 21,2021
Dimitris
Koukoulopoulos
University: Université de Montréal City: Canada Arrival and Departure: Feb 7 - Mar 13, 2021
Emmanuel
Kowalski
University: ETH Zürich City: Switzerland Arrival and Departure: Jan 11 - Feb 12, 2021
Pär
Kurlberg
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 11 - Apr 30, 2021
Erik
Landstedt
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 11 - Apr 30, 2021
Steve
Lester
University: King's College London City: United Kingdom Arrival and Departure: Jan 18 - Mar 26, 2021
Daniel
Loughran
University: University of Bath City: United Kingdom Arrival and Departure: Mar 21 - Apr 30, 2021
Julian
Lyczak
University: IST Austria City: Austria Arrival and Departure: Mar 21 - Apr 30, 2021
André
Macedo
University: City: Arrival and Departure: Mar 19 - Apr 30, 2021
Alexander
Mangerel
University: The Centre de recherches mathématiques (CRM) City: Canada Arrival and Departure: Jan 11 - Mar 19, 2021
Jens
Marklof
University: University of Bristol City: United Kingdom Arrival and Departure: Feb 9 - Feb 18, 2021
Oscar
Marmon
University: Lund University City: Sweden Arrival and Departure: Mar 29 - Apr 30, 2021
Daniele
Mastrostefano
University: University of Warwick City: United Kingdom Arrival and Departure: Jan 11 - Mar 19, 2021
Kaisa
Matomäki
University: University of Turku City: Finland Arrival and Departure: Feb 7 - Mar 6, 2021
Lilian
Matthiesen
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 11 - Apr 30, 2021
James
Maynard
University: University of Oxford City: United Kingdom Arrival and Departure: Feb 14 - Mar 20, 2021
Patrick
Meisner
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 11 - Apr 30, 2021
Philippe
Michel
University: École Polytechnique Fédérale de Lausanne, EPFL City: Switzerland Arrival and Departure: Jan 23 - Feb 28, 2021
Vladimir
Mitankin
University: Max Planck Institute for Mathematics City: Germany Arrival and Departure: Mar 21 - Apr 30, 2021
Rachel
Newton
University: University of Reading City: United Kingdom Arrival and Departure: Mar 29 - Apr 30, 2021
Jennifer
Park
University: Ohio State University City: United States Arrival and Departure: Mar 29 - Apr 30, 2021
Fabien
Pazuki
University: University of Copenhagen City: Denmark Arrival and Departure: Mar 21 - Apr 30, 2021
Sarah
Peluse
University: Princeton University City: United States Arrival and Departure: Jan 11 - Mar 19, 2021
Ian
Petrow
University: University College London City: United Kingdom Arrival and Departure: Jan 11 - Feb 5, 2021
Lillian
Pierce
University: Duke University City: United States Arrival and Departure: Feb 15 - Mar 19, 2021
Carl
Pomerance
University: Dartmouth College City: Germany Arrival and Departure: Feb 28 - Mar 20, 2021
Maksym
Radziwill
University: University of Texas at Austin City: United States Arrival and Departure: Jan 11 - Mar 28, 2021
Olivier
Ramaré
University: Aix-Marseille University City: France Arrival and Departure: Feb 14 - Mar 20, 2021
Martin
Raum
University: Chalmers/University of Gothenburg City: Sweden Arrival and Departure: Jan 11 - Mar 26, 2021
Morten
Risager
University: University of Copenhagen City: Denmark Arrival and Departure: Jan 11 - Feb 6, 2021
Nick
Rome
University: University of Bristol City: United Kingdom Arrival and Departure: Jan 11 - Apr 30, 2021
Zeev
Rudnick
University: Tel Aviv University City: Israel Arrival and Departure: Jan 11 - Apr 30, 2021
Per
Salberger
University: Chalmers/University of Gothenburg City: Sweden Arrival and Departure: Mar 21 - Apr 30, 2021
Damaris
Schindler
University: Universität Göttingen City: Germany Arrival and Departure: Mar 21 - Apr 30, 2021
Kristian
Seip
University: NTNU - Norwegian University of Science and Technology City: Norway Arrival and Departure: Feb 7 - Mar 19, 2021
Igor
Shparlinskii
University: University of New South Wales City: Australia Arrival and Departure: Jan 11 - Mar 20, 2021
Alexei
Skorobogatov
University: Imperial College London City: United Kingdom Arrival and Departure: Mar 21 - Apr 30, 2021
Anders
Södergren
University: Chalmers/University of Gothenburg City: Sweden Arrival and Departure: Feb 15 - Mar 26, 2021
Efthymios
Sofos
University: University of Glasgow City: United Kingdom Arrival and Departure: Mar 13 - Apr 30, 2021
Andreas
Strömbergsson
University: Uppsala University City: Sweden Arrival and Departure: Jan 11 - Mar 19, 2021
Ramin
Takloo-Bighash
University: University of Illinois at Chicago City: United States Arrival and Departure: Mar 21 - Apr 30, 2021
Sho
Tanimoto
University: Nagoya University City: Japan Arrival and Departure: Apr 18 - Apr 24, 2021
Joni
Teräväinen
University: University of Turku City: Finland Arrival and Departure: Jan 11 - Feb 22, 2021
Jesse
Thorner
University: University of Illinois at Urbana-Champaign City: United States Arrival and Departure: -
Pankaj
Vishe
University: Durham University City: United Kingdom Arrival and Departure: Mar 21 - Apr 10, 2021
Aled
Walker
University: University of Cambridge City: United Kingdom Arrival and Departure: Jan 11 - Apr 30, 2021
Igor
Wigman
University: King's College London City: United Kingdom Arrival and Departure: Jan 11 - Mar 13, 2021
Olivier
Wittenberg
University: Université Paris-Sud City: France Arrival and Departure: Mar 21 - Apr 20, 2021