Universität Bonn

Dual Trimester Program: "Harmonic Analysis and Analytic Number Theory"


May 3 - August 20, 2021

Organizers: Valentin Blomer, Farrell Brumley, Philip Gressman, Marina Iliopoulou, Lillian B. Pierce

Description: Analytic Number Theory is a rich and highly active field, with core areas such as the study of the distribution of primes, Diophantine equations, L-functions and automorphic forms, and also connections to algebraic geometry, the Langlands program, arithmetic statistics, arithmetic geometry, and dynamics. Similarly, harmonic analysis is a rich and highly active field, with core areas such as singular integral operators, oscillatory integrals, restriction and Kakeya problems, time-frequency analysis, and also connections to PDEs, geometric measure theory, incidence geometry, and arithmetic combinatorics.

While connections between Analytic Number Theory and Harmonic Analysis have been visible for many years, very recent powerful observations are opening up striking new approaches and new open questions, which this joint trimester aims to develop. Topics that will be explored at this exciting interface include: the methods of decoupling and efficient congruencing, which have resulted in tour-de-force proofs of the Vinogradov Mean Value Theorem; polynomial methods, which exhibit stunning versatility in addressing problems ranging from exponential sum bounds and counting points on varieties to incidence geometry, the Kakeya problem, and restriction estimates; applications of the circle method to geometric settings, harmonic analysis and ergodic theory; oscillatory integrals both from a geometric perspective in harmonic analysis, and also from the perspective of microlocal analysis and applications to trace formulae and automorphic periods and L-functions; connections between modular forms and discrete geometry, such as the breakthrough resolution of sphere-packing problems in dimensions 8 and 24.

Associated Events:

Hausdorff School: The Circle Method (May 10-14, 17-21, 2021)
Summer School: Polynomial Methods (June 7-17, 2021)
Seminar Series: Arithmetic Applications of Fourier Analysis
Seminar Series: Harmonic Analysis from the Edge


Publications

No.
Author(s)
Title
Preprint
Publication
2021b01 Oliveira e Silva, D.; Mandel, R. The Tomas-Stein Inequality under the effect of symmetries 2106.08255 JAMA 150 (2023), 547–582, https://doi.org/10.1007/s11854-023-0282-3
2021b02 Krause, B.; Roos, J. Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: Lp bounds for p>1 2107.14616 Journal of Functional Analysis 285 (2023), no. 10, 110123, https://doi.org/10.1016/j.jfa.2023.110123
2021b03 Greenfeld, R.; Tao, T. Undecidable translational tilings with only two tiles, or one nonabelian tile 2108.07902 Discrete Comput Geom 70 (2023), 1652–1706, https://doi.org/10.1007/s00454-022-00426-4
2021b04 Nelson, P. Bounds for standard L-functions 2109.15230
2021b05 Bilz, C.; Weigt, J. The one-dimensional centred maximal function diminishes the variation of indicator functions 2107.12404  
2021b06 Gonçalves, F.; Greenfeld, R.; Madrid, J. Generalized Collatz Maps with Almost Bounded Orbits 2111.06170  
2021b07 Domínguez, Ó; Seeger, A.; Street, B.; Van Schaftingen, J.; Lam Yung, P. Spaces of Besov-Sobolev type and a problem on nonlinear approximation 2112.05539 Journal of Functional Analysis 284(4) (2023), 109775, https://doi.org/10.1016/j.jfa.2022.109775
2021b08 Brezis, H.; Seeger, A.; Van Schaftingen, J.; Lam Yung, P. Families of functionals representing Sobolev norms 2109.02930 to appear soon in Analysis & PDE
2021b09 de Dios, J.; Greenfeld, R.; Ivanisvili, P.; Madrid, J. Additive energies on discrete cubes 2112.09352
2021b10 Peluse, S. Subsets of Fnp×Fnp without L-shaped configurations 2205.01295
2021b11 Roos, J.; Seeger, A.; Srivastava, R. Spherical maximal operators on Heisenberg groups: Restricted dilation sets 2208.02774 Studia Mathematica 273 (2023), 1-28, https://doi.org/10.4064/sm220804-22-6
2021b12 Greenfeld, R.; Iliopoulou, M.; Peluse, S. On integer distance sets 2401.10821
 
2021b13 Ramaré, O. Notes on restriction theory in the primes

2109.10180
 

Israel Journal of Mathematics TBD (2023), 1–22, https://doi.org/10.1007/s11856-023-2586-5


Participants

Name
Affiliation
Jitendra Bajpai TU Dresden
Christian Bernert University of Göttingen
Constantin Bilz University of Birmingham
Valentin Blomer Universität Bonn
Cynthia Bortolotto ETH Zürich
Julia Brandes Chalmers / University of Gothenburg
Claire Burrin ETH Zurich
Paul Buterus Bielefeld University
Alan Chang Princeton University
Mateus Costa de Sousa Basque Center for Applied Mathematics
Jaume de Dios Pont University of California Los Angeles
Kevin Destagnol Université Paris Saclay
Robert Fraser University of Edinburgh
Javier Fresán École polytechnique
Ayla Gafni University of Mississippi
João Pedro Gonçalves Ramos ETH Zürich
Rachel Greenfeld Institute for Advanced Study
Rok Havlas University of Göttingen
Harald Andres Helfgott Georg-August Universität Göttingen
Leonhard Hochfilzer University of Göttingen
Kevin Hughes University of Bristol
Marina Iliopoulou University of Birmingham
Hongki Jung Indiana University
Miriam Sophie Kaesberg Georg-August Universtität Göttingen
Emmanuel Kowalski ETH Zürich
Erez Lapid Weizmann Institute of Science
Didier Lesesvre Sun Yat-Sen University
Zane Li Indiana University Bloomington
Yongxiao Lin EPFL
Akos Magyar University of Georgia
Jasmin Matz University of Copenhagen
Philippe Michel Ecole Polytechnique Federale de Lausanne (EPFL)
Bart Michels Université Sorbonne Paris Nord
Diogo Oliveira e Silva University of Birmingham
Andrea Olivo International Centre for Theoretical Physics (ICTP)
Sarah Peluse Princeton University
Olivier Ramaré CNRS / Université Aix-Marseille
Joris Roos University of Massachusetts Lowell
Alisa Sedunova Saint Petersburg State Univercity
Andreas Seeger University of Wisconsin-Madison
Rajula Srivastava University of Wisconsin, Madison
Terence Tao Department of Mathematics, UCLA
Niclas Technau University of Madison-Wisconsin
Lola Thompson Universiteit Utrecht
Poster TP_2021_05
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