Arithmetic (and) Harmonic Analysis (Web)
May 31 - June 4, 2021
Fourier-theoretic methods play a pervasive role in analytic number theory, thus linking the field intimately with that of harmonic analysis. Consequently, there has long been a transfer of technology between the two fields, giving new impulses to either side. Recently, simultaneous proofs of Vinogradov’s mean value theorem, a cornerstone result in both fields, have increased the momentum of this transfer of technologies and have created a flurry of activity aimed at better understanding how the two proofs are related and how they may be generalised. The goal of the workshop is both to provide a forum in which participants can be informed about recent developments and to give the opportunity to exchange ideas that can lead to a better “dictionary” between the two methods as well as potential generalisations. We are confident that such a setup will contribute to a deeper understanding of the topic at hand and related problems, as well as serve the wider purpose of easing communication between the two fields.
Hughes: Initial approaches to discrete restriction theory.
Shparlinski: Maximal Operators and Restriction Bounds for Weyl Sums
Seminars
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Roth’s theorem: using harmonic analysis to count solutions to a linear equation in sets of integers May 31 10:00 - 10:40 -
Magic functions and the equidistribution of zeros of polynomials May 31 11:00 - 11:40 Magic functions and the equidistribution of zeros of polynomials
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Efficient congruencing: inductive application of linearity in Henselian fields May 31 15:00 - 16:00 Efficient congruencing: inductive application of linearity in Henselian fields
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Demeter May 31 16:30 - 17:30 Demeter
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Initial approaches to discrete restriction theory June 01 10:00 - 10:40 Initial approaches to discrete restriction theory
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Maximal Operators and Restriction Bounds for Weyl Sums June 01 11:00 - 11:40 Maximal Operators and Restriction Bounds for Weyl Sums
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Wooley June 01 15:00 - 16:00 Wooley
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Demeter June 01 16:30 - 17:30 Demeter
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On sums of unlike powers June 02 10:00 - 10:40 On sums of unlike powers
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Decoupling for quadratic forms June 02 11:00 - 11:40 Decoupling for quadratic forms
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Embedding metric graphs in “thin sets” June 02 14:00 - 14:40 Embedding metric graphs in “thin sets”
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Problem and discussion session June 02 15:00 - 17:30 Problem and discussion session
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Improved discrete restriction for the parabola June 03 10:00 - 10:40 Improved discrete restriction for the parabola
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Ellipsephic Efficient Congruencing for the Vinogradov system June 03 11:00 - 11:40 Ellipsephic Efficient Congruencing for the Vinogradov system
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Wooley June 03 15:00 - 16:00 Wooley
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Demeter June 03 16:30 - 17:30 Demeter
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Weyl sums: remarks and speculations June 04 10:00 - 10:40 Weyl sums: remarks and speculations
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Sharp L^p estimates for oscillatory integral operators of arbitrary signature June 04 11:00 - 11:40 Sharp L^p estimates for oscillatory integral operators of arbitrary signature
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Problem and discussion session June 04 15:00 - 17:30 Problem and discussion session
Participants
| Name | University | Country | Arrival and Departure |
|---|---|---|---|
| Theresa Anderson | University: Purdue University | City: United States | Arrival and Departure: - |
| Kirsti Biggs | University: Chalmers / University of Gothenburg | City: Sweden | Arrival and Departure: - |
| Julia Brandes | University: Chalmers / University of Gothenburg | City: Sweden | Arrival and Departure: - |
| Tony Carbery | University: University of Edinburgh | City: United Kingdom | Arrival and Departure: - |
| Emanuel Carneiro | University: University of Trieste | City: Italy | Arrival and Departure: - |
| Mei-Chu Chang | University: University of California, Riverside | City: United States | Arrival and Departure: - |
| Ciprian Demeter | University: Indiana University Bloomington | City: United States | Arrival and Departure: - |
| Shaoming Guo | University: University of Wisconsin | City: United States | Arrival and Departure: - |
| Brandon Hanson | University: The University of Georgia | City: United States | Arrival and Departure: - |
| Kevin Hughes | University: University of Bristol | City: United Kingdom | Arrival and Departure: - |
| Marina Iliopoulou | University: University of Kent | City: United Kingdom | Arrival and Departure: - |
| Angel Kumchev | University: Towson University | City: United States | Arrival and Departure: - |
| Zane Li | University: Indiana University Bloomington | City: United States | Arrival and Departure: - |
| Yu-ru Liu | University: University of Waterloo | City: United Kingdom | Arrival and Departure: - |
| Akos Magyar | University: The University of Georgia | City: United States | Arrival and Departure: - |
| Akshat Mudgal | University: Purdue University | City: United States | Arrival and Departure: - |
| Simon Myerson | University: Universität Göttingen | City: Germany | Arrival and Departure: - |
| Changkeun Oh | University: University of Wisconsin | City: United States | Arrival and Departure: - |
| Scott Parsell | University: West Chester University | City: United States | Arrival and Departure: - |
| Lillian Pierce | University: Duke University | City: United States | Arrival and Departure: - |
| Javier Pliego | University: Purdue University | City: United States | Arrival and Departure: - |
| Javier Pliego | University: University of Bristol | City: United Kingdom | Arrival and Departure: - |
| Sean Prendiville | University: Lancaster University | City: United Kingdom | Arrival and Departure: - |
| Olivier Robert | University: Université Jean Monnet | City: France | Arrival and Departure: - |
| Igor Shparlinski | University: University of New South Wales | City: Australia | Arrival and Departure: - |
| Olof Sisask | University: Stockholm University | City: Sweden | Arrival and Departure: - |
| Hong Wang | University: Institute for Advanced Study, IAS | City: United States | Arrival and Departure: - |
| Trevor Wooley | University: Purdue University | City: United States | Arrival and Departure: - |
| Po-Lam Yung | University: Australian National University | City: Australia | Arrival and Departure: - |
| Ruixiang Zhang | University: University of Wisconsin | City: United States | Arrival and Departure: - |
| Lilu Zhao | University: Shandong University | City: China | Arrival and Departure: - |
| Pavel Zorin-Kranich | University: University of Bonn | City: Germany | Arrival and Departure: - |