Analytic Number Theory

January 17 - April 26, 2024

Analytic Number Theory has seen numerous breakthroughs on very fundamental questions during recent years. These include spectacular results on progressions in the primes and prime gaps both large and small. Apart from prime number theory, multiplicative number theory has also seen major progress, for example several breakthroughs on multiplicative functions in short intervals, e.g. relating to the Erdős Discrepancy problem. The theory of automorphic forms and their L-functions is also central in modern number theory, linking diverse areas of mathematics like analysis, representation theory, algebraic geometry to name a few. Recently there have been several strong results about moments of central L-values supporting random matrix theory predictions, results on equidistribution and other types of distributions, density theorems verifying cases of Sarnak’s conjecture, and many other remarkable advances.

Workshops during the thematic semester:

  • Kick-off workshop: January 22 – 26, 2024
  • Middle workshop: March 11 – 15, 2024

Seminars Scroll to the next upcoming seminar

  • Maksym Radziwill: Recent progress in multiplicative number theory January 18 13:15 - 14:15

    Maksym Radziwill: Recent progress in multiplicative number theory

  • Workshop: Ranks of matrices with polynomial entries, Igor Shparlinski January 22 09:30 - 10:30

    Workshop: Ranks of matrices with polynomial entries, Igor Shparlinski

  • Workshop: Autocorrelation of Hurwitz Class Numbers, Alex Walker January 22 11:00 - 12:00

    Workshop: Autocorrelation of Hurwitz Class Numbers, Alex Walker

  • Workshop: Bias in the running time of the Euclidean algorithm and applications to Dedekind sums, Paolo Minelli January 22 13:30 - 14:30

    Workshop: Bias in the running time of the Euclidean algorithm and applications to Dedekind sums, Paolo Minelli

  • Workshop: The sixth moment of Dirichlet L-functions, Maksym Radziwill January 22 15:00 - 16:00

    Workshop: The sixth moment of Dirichlet L-functions, Maksym Radziwill

  • Workshop: Hyperbolic lattice point counting in unbounded rank, Valentin Blomer January 23 09:30 - 10:30

    Workshop: Hyperbolic lattice point counting in unbounded rank, Valentin Blomer

  • Workshop: The prime geodesic theorem in arithmetic progressions, Gergely Harcos January 23 11:00 - 12:00

    Workshop: The prime geodesic theorem in arithmetic progressions, Gergely Harcos

  • Workshop: Toroidal averages with Dirichlet characters, Emmanuel Kowalski January 23 13:30 - 14:30

    Workshop: Toroidal averages with Dirichlet characters, Emmanuel Kowalski

  • Workshop: On the local L2-bound of the Eisenstein series and application, Subhajit Jana January 23 15:00 - 16:00

    Workshop: On the local L2-bound of the Eisenstein series and application, Subhajit Jana

  • Workshop: Mass equidistribution for Siegel modular forms, Steve Lester January 24 09:00 - 10:00

    Workshop: Mass equidistribution for Siegel modular forms, Steve Lester

  • Workshop: Sums of odd-ly many fractions and the distribution of primes, Vivian Kuperberg January 24 10:30 - 11:30

    Workshop: Sums of odd-ly many fractions and the distribution of primes, Vivian Kuperberg

  • Workshop: Correlations of multiplicative functions along Beatty sequences, Aled Walker January 24 11:40 - 12:10

    Workshop: Correlations of multiplicative functions along Beatty sequences, Aled Walker

  • Workshop: On some arithmetic statistics for integer matrices, Alina Ostafe January 25 09:30 - 10:30

    Workshop: On some arithmetic statistics for integer matrices, Alina Ostafe

  • Workshop: Non-vanishing of twists of L-functions by characters of fixed order, Asbjørn Nordentoft January 25 11:00 - 12:00

    Workshop: Non-vanishing of twists of L-functions by characters of fixed order, Asbjørn Nordentoft

  • Workshop: Distributional properties of smooth numbers: Smooth numbers are orthogonal to nilsequences, Lilian Matthiesen January 25 13:30 - 14:30

    Workshop: Distributional properties of smooth numbers: Smooth numbers are orthogonal to nilsequences, Lilian Matthiesen

  • Workshop: Six-dimensional sphere packing and linear programming, Matthew de Courcy-Ireland January 25 15:00 - 16:00

    Workshop: Six-dimensional sphere packing and linear programming, Matthew de Courcy-Ireland

  • Workshop: On the distribution of closed geodesic cycle integrals and non-vanishing of central val, Petru Constantinescu January 26 09:30 - 10:30

    Workshop: On the distribution of closed geodesic cycle integrals and non-vanishing of central val, Petru Constantinescu

  • Workshop: Weighted statistics of families of L-functions, Alessandro Fazzari January 26 11:00 - 12:00

    Workshop: Weighted statistics of families of L-functions, Alessandro Fazzari

  • Workshop: Cubic weyl sums with smooth denominator, Bryce Kerr January 26 13:30 - 14:30

    Workshop: Cubic weyl sums with smooth denominator, Bryce Kerr

  • Workshop: Detecting primes in multiplicatively structured sequences, Joni Teräväinen January 26 15:00 - 16:00

    Workshop: Detecting primes in multiplicatively structured sequences, Joni Teräväinen

  • Johan Andersson: Aspects of universality January 31 13:00 - 13:50

    Johan Andersson: Aspects of universality

  • Kaisa Matomäki: Mollifying Dirichlet L-functions and their derivatives January 31 14:00 - 14:50

    Kaisa Matomäki: Mollifying Dirichlet L-functions and their derivatives

  • Sun Kai Leung: Joint distribution of primes in multiple short intervals February 02 11:00 - 11:50

    Sun Kai Leung: Joint distribution of primes in multiple short intervals

  • Yoonbok Lee: Discrepancy bounds for the distribution of L-functions near the critical line February 07 13:00 - 13:50

    Yoonbok Lee: Discrepancy bounds for the distribution of L-functions near the critical line

  • Giacomo Cherubini: Coprime-universal quadratic forms February 07 14:00 - 14:50

    Giacomo Cherubini: Coprime-universal quadratic forms

  • Manuel Hauke: The Duffin-Schaeffer conjecture and beyond February 09 10:00 - 10:50

    Manuel Hauke: The Duffin-Schaeffer conjecture and beyond

  • Sumit Kumar: Delta method and its application to the Rankin-Selberg problem February 09 11:00 - 11:50

    Sumit Kumar: Delta method and its application to the Rankin-Selberg problem

  • Dimitrios Chatzakos: Mean values and quantum variance for degenerate Eisenstein series of higher rank February 14 13:00 - 13:50

    Dimitrios Chatzakos: Mean values and quantum variance for degenerate Eisenstein series of higher rank

  • Min Lee: Murmurations of holomorphic modular forms in the weight aspect February 14 14:00 - 14:50

    Min Lee: Murmurations of holomorphic modular forms in the weight aspect

  • Athanasios Sourmelidis: Discrete Omega results for the Riemann zeta function February 16 10:00 - 10:50

    Athanasios Sourmelidis: Discrete Omega results for the Riemann zeta function

  • Oleksiy Klurman: Counting sign changes February 16 11:10 - 12:00

    Oleksiy Klurman: Counting sign changes

  • Sebastián Herrero: Special values of Green’s functions on hyperbolic 3-space February 21 13:00 - 13:50

    Sebastián Herrero: Special values of Green’s functions on hyperbolic 3-space

  • Ilaria Viglino: Almost sure convergence of least common multiple of ideals for polynomials over a number field February 21 14:10 - 15:00

    Ilaria Viglino: Almost sure convergence of least common multiple of ideals for polynomials over a number field

  • Prahlad Sharma: Bilinear sums with (GL(2)) coefficients and the exponent of distribution of (d_3) February 23 10:00 - 10:50

    Prahlad Sharma: Bilinear sums with (GL(2)) coefficients and the exponent of distribution of (d_3)

  • Danylo Radchenko: Convolution identities for sums of even powers of divisors February 28 13:00 - 13:50

    Danylo Radchenko: Convolution identities for sums of even powers of divisors

  • Robert Tichy: Equidistribution and Pseudorandomness February 28 14:00 - 14:50

    Robert Tichy: Equidistribution and Pseudorandomness

Participants

Name University Country Arrival and Departure
Keshav
Aggaval
University: University of Copenhagen City: Denmark Arrival and Departure: February 26, Mar 10 - March 2, Mar 16, 2024
Johan
Andersson
University: Örebro University City: Sweden Arrival and Departure: Jan 21, Mar 17 - Feb 4, Mar 28, 2024
Nuno
Arala Santos
University: University of Warwick City: United Kingdom Arrival and Departure: Mar 17 - Apr 27, 2024
Jacques
Benatar
University: University of Helsinki City: Finland Arrival and Departure: Feb 18 - Feb 29, 2024
Sandro
Bettin
University: University of Genova City: Italy Arrival and Departure: Feb 5 - Feb 16, 2024
Andras
Biro
University: Alfréd Rényi Institute of Mathematics City: Hungary Arrival and Departure: Apr 7 - Apr 21, 2024
Valentin
Blomer
University: University of Bonn City: Germany Arrival and Departure: Jan 19 - Jan 25, 2024
Andrii
Bondarenko
University: Norwegian University of Science and Technology City: Norway Arrival and Departure: Jan 31, Mar 31 - Mar 1, Apr 26, 2024
Matteo
Bordignon
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 17 - Apr 26, 2024
Julia
Brandes
University: Chalmers/University of Gothenburg City: Sweden Arrival and Departure: March 18 - April 7, 2024
Timothy
Browning
University: Institute of Science and Technology Austria (ISTA) City: Austria Arrival and Departure: Mar 18 - Apr 8, 2024
Claire
Burrin
University: University of Zurich City: Switzerland Arrival and Departure: Mar 11 - Mar 18, 2024
Mattias
Byléhn
University: Chalmers/University of Gothenburg City: Sweden Arrival and Departure: Feb 19 - Feb 25, 2024
Dimitrios
Chatzakos
University: University of Patras City: Greece Arrival and Departure: Feb 10 - Feb 18, 2024
Giacomo
Cherubini
University: INdAM City: Italy Arrival and Departure: Feb 4 - Feb16, 2024
Jake
Chinis
University: University of Bristol City: United Kingdom Arrival and Departure: Jan 17 - Apr 26, 2024
Petru
Constantinescu
University: École Polytechnique Fédérale de Lausanne City: Switzerland Arrival and Departure: Jan 19 - Apr 26, 2024
Matthew
de Courcy-Ireland
University: Stockholm University City: Sweden Arrival and Departure: Jan 17 - Apr 26, 2024
Prandendu
Darbar
University: Norwegian University of Science and Technology City: Norway Arrival and Departure: Feb 4, Mar 19 - Feb 13, Mar 31, 2024
Shreyasi
Datta
University: Uppsala University City: Sweden Arrival and Departure: Jan 21 - Apr 19, 2024
Lucile
Devin
University: Université du Littoral Côte d'Opale City: France Arrival and Departure: Mar 4 - Mar 17, 2024
Sary
Drappeau
University: I2M, Univ Aix-Marseille City: France Arrival and Departure: Mar 2 - Mar 9, 2024
Anne-Maria
Ernvall-Hytönen
University: University of Helsinki City: Finland Arrival and Departure: Mar 3 - Mar 19, 2024
Alessandro
Fazzari
University: Université de Montréal City: Canada Arrival and Departure: Jan 19 - Apr 17, 2024
Daniel
Fiorilli
University: Université Paris-Saclay City: France Arrival and Departure: Mar 2 - Mar 10, 2024
Maxim
Gerspach
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 17 - April 26, 2024
Alia
Hamieh
University: University of Northern British Columbia City: Canada Arrival and Departure: Feb 24 - Mar 16, 2024
Gergely
Harcos
University: Alfréd Rényi Institute of Mathematics City: Hungary Arrival and Departure: Jan 18 - Feb 4, 2024
Adam
Harper
University: University of Warwick City: United Kingdom Arrival and Departure: Feb 15 - Apr 6, 2024
Manuel
Hauke
University: Graz University of Technology City: Austria Arrival and Departure: Jan 16 - Mar 21, 2024
Winston
Heap
University: NTNU City: Norway Arrival and Departure: Feb 18 - Mar 9, 2024
Roger
Heath-Brown
University: Oxford University City: United Kingdom Arrival and Departure: Mar 9 - Mar 30, 2024
Sebastián
Herrero
University: University of Santiago de Chile/ETH Zürich City: Chile/Switzerland Arrival and Departure: Feb 19 - Feb 27, 2024
Bingrong
Huang
University: Shandong University City: China Arrival and Departure: Feb 4, Mar 20 - Mar 9, April 12, 2024
Ozlem
Immamoglu
University: ETH Zurich City: Switzerland Arrival and Departure: Apr 14 - Apr 26, 2024
Subhajit
Jana
University: Queen Mary University of London City: United Kingdom Arrival and Departure: Jan 21 - Apr 19, 2024
Florent
Jouve
University: Institut de mathématiques de Bordeaux City: France Arrival and Departure: Apr 17 - Apr 26, 2024
Jesse
Jääsaari
University: University of Turku City: Finland Arrival and Departure: Feb 17 - Mar 2, 2024
Jon
Keating
University: University of Oxford City: United Kingdom Arrival and Departure: Apr 1 - Apr 12, 2024
Bryce
Kerr
University: University of New South Wales City: Australia Arrival and Departure: Jan 22 - Feb 22, 2024
Oleksiy
Klurman
University: University of Bristol City: United Kingdom Arrival and Departure: Jan 17 - Apr 26, 2024
Emmanuel
Kowalski
University: ETH Zürich City: Switzerland Arrival and Departure: Jan 17 - Jan 31, 2024
Sumit
Kumar
University: Alfréd Rényi Institute of Mathematics City: Hungary Arrival and Departure: Jan 16, Mar 29 - Feb 14, Apr 26, 2024
Vinay
Kumaraswamy
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 22 - Apr 26, 2024
Vivian
Kuperberg
University: ETH Zurich City: Switzerland Arrival and Departure: Jan 17, Mar 20 - Feb 10, Apr 6, 2024
Pär
Kurlberg (Organizer)
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 17 - Apr 26, 2024
Chung-Hang
Kwan
University: University College London City: United Kingdom Arrival and Departure: Feb 11, Mar 17 - Feb 18, Apr 26, 2024
Min
Lee
University: University of Bristol City: United Kingdom Arrival and Departure: Feb 6 - Feb 17, 2024
Yoonbok
Lee
University: Incheon National University City: Korea Arrival and Departure: Feb 3 - Feb 17, 2024
Steve
Lester
University: King's College London City: United Kingdom Arrival and Departure: Jan 18 - Mar 1, 2024
Sun Kai
Leung
University: University of Montreal City: Canada Arrival and Departure: Jan 17 - Apr 26, 2024
Kaisa
Matomäki
University: University of Turku City: Finland Arrival and Departure: Jan 29, Apr 8 - Feb 2, Apr 12, 2024
Lilian
Matthiesen
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 17 - Apr 26, 2024
Philippe
Michel
University: Ecole Polytechnique Federale de Lausanne City: Switzerland Arrival and Departure: Mar 27 - Apr 14, 2024
Paolo
Minelli
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 17 - Apr 26, 2024
Paul
Nelson
University: Aarhus University City: Denmark Arrival and Departure: Apr 9 - Apr 26, 2024
Asbjørn
Nordentoft
University: Université Paris 13 City: France Arrival and Departure: Jan 21 - Jan 28, 2024
Alina
Ostafe
University: UNSW Sidney City: Australia Arrival and Departure: Jan 21 - Jan 30, 2024
Neea
Palojärvi
University: University of Helsinki City: Finland Arrival and Departure: Feb 23 - Mar 2, 2024
Fabien
Pazuki
University: University of Copenhagen City: Denmark Arrival and Departure: Feb 29 - Mar 7, 2024
Yiannis
Petridis
University: University College London City: United Kingdom Arrival and Departure: Jan 21, March 1 - Jan 28, Mar 29, 2024
Ian
Petrow
University: University College London City: United Kingdom Arrival and Departure: Apr 14 - Apr 26, 2024
Lillian
Pierce
University: Duke University City: United States Arrival and Departure: Mar 10 - Mar 23, 2024
Anke
Pohl
University: University of Bremen City: Germany Arrival and Departure: Mar 10 - Mar 16, 2024
Danylo
Radchenko
University: University of Lille City: France Arrival and Departure: Feb 25 - Mar 1, 2024
Maksym
Radziwill
University: University of Texas at Austin City: United States Arrival and Departure: Jan 17 - February 21, 2024
Morten
Risager (Organizer)
University: University of Copenhagen City: Denmark Arrival and Departure: Jan 17 - Apr 26, 2024
Brad
Rodgers
University: Queens University City: Canada Arrival and Departure: Mar 30 - Apr 26, 2024
Abhishek
Saha
University: Queen Mary University of London City: United Kingdom Arrival and Departure: Mar 3 - Mar 16, 2024
Eero
Saksman
University: University of Helsinki City: Finland Arrival and Departure: Mar 4 - Mar 9, 2024
Per
Salberger
University: Chalmers University of Technology City: Sweden Arrival and Departure: Mar 10 - Apr 6, 2024
Kristian
Seip
University: Norwegian University of Science and Technology City: Norway Arrival and Departure: Jan 17 - Feb 16, 2024
Arul
Shankar
University: University of Toronto City: Canada Arrival and Departure: Mar 10 - Mar 24, 2024
Prahlad
Sharma
University: Alfréd Rényi Institute of Mathematics City: Hungary Arrival and Departure: Jan 22, Apr 20 - Feb 27, Apr 26, 2024
Igor
Shparlinski
University: University of New South Wales City: Australia Arrival and Departure: Jan 15 - Apr 27, 2024
Andrei
Shubin
University: Vienna University of Technology City: Austria Arrival and Departure: Jan 15 - Apr 27, 2024
Efthymios
Sofos
University: Glasgow University City: United Kingdom Arrival and Departure: April 7 - April 14, 2024
Athanasios
Sourmelidis
University: Graz University of Technology City: Austria Arrival and Departure: Jan 21 - Mar 17, 2024
Julia
Stadlmann
University: University of Oxford City: United Kingdom Arrival and Departure: Mar 17 - Apr 26, 2024
Andreas
Strömbergsson
University: Uppsala University City: Sweden Arrival and Departure: Jan 17 - Apr 26, 2024
Anders
Södergren (Organizer)
University: Chalmers/University of Gothenburg City: Sweden Arrival and Departure: Jan 15 - Apr 26, 2024
Barnabás
Szabó
University: University of Warwick City: United Kingdom Arrival and Departure: Mar 1 - Apr 26, 2024
Niclas
Technau
University: Max Planck Institute for Mathematics City: Germany Arrival and Departure: Feb 15, Apr 1 - Mar 9, Apr 13, 2024
Joni
Teräväinen
University: University of Turku City: Finland Arrival and Departure: Jan 17 - Apr 26, 2024
Robert
Tichy
University: TU Graz City: Austria Arrival and Departure: Feb 19 - Feb 29, 2024
Caroline
Turnage-Butterbaugh
University: Carleton College City: United States Arrival and Departure: Mar 10 - Mar 19, 2024
Ilaria
Viglino
University: EPFL Lausanne City: Switzerland Arrival and Departure: Feb 18 - Feb 25, 2024
Pankaj
Vishe
University: Durham University City: United Kingdom Arrival and Departure: Apr 1 - Apr 15, 2024
Aled
Walker
University: King's College London City: United Kingdom Arrival and Departure: Jan 20, Mar 2, Apr 2 - Feb 23, Mar 24, Apr 19, 2024
Alexander
Walker
University: University College London City: United Kingdom Arrival and Departure: Jan 21 - Mar 16, 2024
Markus
Valås Hagen
University: Norwegian University of Science and Technology City: Norway Arrival and Departure: Apr 22 - Apr 26, 2024
Igor
Wigman
University: King's College London City: United Kingdom Arrival and Departure: Jan 21, April 2 - Jan, 27, Apr 20, 2024
Trevor
Wooley
University: Purdue University City: United States Arrival and Departure: Mar 10 - Mar 23, 2024

Preprints

  1. Critical exponents of the Riesz projection - Ole Fredrik Brevig Adrián Llinares Kristian Seip