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

Ciprian Demeter

Zhao

Zorin-Kranich

Seminars Scroll to the next upcoming seminar

  • Roth’s theorem: using harmonic analysis to count solutions to a linear equation in sets of integers May 31 10:00 - 10:40

    Roth’s theorem: using harmonic analysis to count solutions to a linear equation in sets of integers

  • Magic functions and the equidistribution of zeros of polynomials May 31 11:00 - 11:40

    Magic functions and the equidistribution of zeros of polynomials

  • Efficient congruencing: inductive application of linearity in Henselian fields May 31 15:00 - 16:00

    Efficient congruencing: inductive application of linearity in Henselian fields

  • Demeter May 31 16:30 - 17:30

    Demeter

  • Initial approaches to discrete restriction theory June 01 10:00 - 10:40

    Initial approaches to discrete restriction theory

  • Maximal Operators and Restriction Bounds for Weyl Sums June 01 11:00 - 11:40

    Maximal Operators and Restriction Bounds for Weyl Sums

  • Wooley June 01 15:00 - 16:00

    Wooley

  • Demeter June 01 16:30 - 17:30

    Demeter

  • On sums of unlike powers June 02 10:00 - 10:40

    On sums of unlike powers

  • Decoupling for quadratic forms June 02 11:00 - 11:40

    Decoupling for quadratic forms

  • Embedding metric graphs in “thin sets” June 02 14:00 - 14:40

    Embedding metric graphs in “thin sets”

  • Problem and discussion session June 02 15:00 - 17:30

    Problem and discussion session

  • Improved discrete restriction for the parabola June 03 10:00 - 10:40

    Improved discrete restriction for the parabola

  • Ellipsephic Efficient Congruencing for the Vinogradov system June 03 11:00 - 11:40

    Ellipsephic Efficient Congruencing for the Vinogradov system

  • Wooley June 03 15:00 - 16:00

    Wooley

  • Demeter June 03 16:30 - 17:30

    Demeter

  • Weyl sums: remarks and speculations June 04 10:00 - 10:40

    Weyl sums: remarks and speculations

  • 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

  • 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: -