Fourier Analysis @200

Home > Workshops > 2022 > Fourier Analysis @200

Fourier Analysis @200

 27 Jun - 01 Jul 2022

Appleton Tower, University of Edinburgh


  • Neal Bez, Saitama University
  • Aline Bonami, University of Orleans
  • Michael Cowling , University of New South Wales
  • Spyridon Dendrinos, University College Cork
  • Jonathan Hickman, University of Edinburgh
  • Betsy Stovall, University of Wisconsin-Madison


This workshop marked the bicentennial of the publication of Fourier's Theorie analytique de la chaleur, a seminal scientific work which has had a profound impact on the modern world. In this treatise Fourier famously introduced the series decomposition which now bears his name. Over the intervening two hundred years, Fourier's ideas have played a fundamental role in science and engineering, whilst the mathematical questions which arose from his work, and the need to place the theory on a rigorous foundation, dominated much of nineteenth and twentieth century mathematical analysis.

It is fitting that the anniversary of the Theorie analytique de la chaleur coincided with one of the most remarkably active periods in the modern development of Fourier's theory, as encompassed by the field of euclidean harmonic analysis. During the last five years, a wave of revolutionary new ideas have transformed our understanding of the Fourier transform and, furthermore, important and surprising connections have been forged between harmonic analysis and a variety of other mathematical disciplines with spectacular consequences. This has led, for instance, to deep insights into the behaviour of solutions of wave and Schrodinger equations, the resolution of the long-standing Vinogradov mean value conjecture from analytic number theory and significant progress on fundamental questions from geometric measure theory such as the Kakeya conjecture and Falconer's distance problem. In light of these fast moving developments, and in order to further cultivate this remarkable burst of activity, it is crucial to hold regular international meetings, bringing together experts from across the globe. Edinburgh, as a world leading centre for harmonic analysis, was ideally placed to host this workshop.

The workshop also celebrated the contributions of James Wright (University of Edinburgh) to modern harmonic analysis, which include numerous and highly significant results on the theory of Fourier multipliers, oscillatory integrals and interactions between harmonic analysis and number theory.

As a satellite event there was a 2-day Young Researchers Symposium at Appleton Tower in Edinburgh, 23rd June - 24th June 2022.


Recorded Talks


Monday 27 June 2022
Registration with Refreshments
Welcome and Housekeeping
Tony Carbery , University of Edinburgh The Mizohata--Takeuchi conjecture: an overview
Joshua Zahl , University of British Columbia New Kakeya bounds using multilinear and plany estimates
Lunch at Appleton Tower
Sanghyuk Lee , Seoul National University Sharp smoothing estimates for averages over curves
Marina Iliopoulou , University of Birmingham Some small progress on the Mizohata-Takeuchi conjecture
Detlef Müller, University of Kiel Maximal averages along hypersurfaces: a ``geometric conjecture'' and further progress for 2-surfaces
Informal Welcome Reception in Appleton Tower Concourse Welcome reception ends 18.30
Tuesday 28 June 2022
Jonathan Bennett, University of Birmingham A tomographic perspective on Fourier extension operators
Sarah Peluse , Princeton University Bounds for subsets of $\mathbb{F}_p^n \times \mathbb{F}_p^n$ without L-shaped configurations
Nir Lev , Bar-Ilan University Fuglede's tiling-spectrality conjecture for convex domains
Lunch in Appleton Tower
Eero Saksman , University of Helsinki Homogenization of Quasiconformal Maps via Singular Integrals
Julia Wolf, University of Cambridge Efficient regularity lemmas in higher-order Fourier analysis
Lillian Pierce , Duke University Counterexamples disproving pointwise convergence for solutions of dispersive PDE’s
Historical Lecture by Jean Dhombres , The School for Advanced Studies in the Social Sciences, Paris Fourier's hieroglyphs: those of Egypt, of politics and of mathematics
Drinks Reception at Appleton Tower Reception Ends 20.00
Wednesday 29 June 2022
Terence Tao , University of California, Los Angeles The structure of translational tilings
Mariusz Mirek , Rutgers University Multiple and multi-parameter pointwise ergodic theory
Alexander Olevskii , Tel Aviv University Fourier convergence and homeomorphisms of the circle
Lunch at Appleton Tower
Free afternoon for participants
Thursday 30 June 2022
Michael Christ , University of California, Berkeley On implicitly oscillatory quadrilinear integrals
Ana Vargas , Universidad Autónoma de Madrid On Restriction of the Fourier Transform to Surfaces with Negative Curvature
Gian Maria Dall'Ara , Scuola Normale Superiore (Pisa) Sharp subelliptic estimates via an uncertainty principle
Lunch at appleton Tower
Andreas Seeger , University of Wisconsin–Madison Variation bounds for spherical means and sparse domination
Victor Lie , Purdue University The LGC method
Hong Wang, University of California, Los Angeles Projection theorems and applications
Conference Dinner at South Hall, Pollock Halls
Friday 1 July 2022
Malabika Pramanik, University of British Columbia Hausdorff dimension and curved patterns
Brian Street , University of Wisconsin–Madison Maximal Subellipticity
Philip Gressman , University of Pennsylvania Radon-Brascamp-Lieb Inequalities and Model Operators
Packed Lunch
End of Workshop

Sponsors and Funders:

  • Ems
  • title=
  • title=
  • Heilbronn
  • title=
  • title=
  • title=
  • title=