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

  • 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