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
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 | to appear soon in Indiana University Mathematics Journal |
| 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 | Discrete Analysis (2023), https://doi.org/10.19086/da.84737 |
| 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 | Israel Journal of Mathematics TBD (2023), 1–22, https://doi.org/10.1007/s11856-023-2586-5 | |
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 |
