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Neal Bez, Saitama University
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Aline Bonami, University of Orleans
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Michael Cowling , University of New South Wales
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Spyridon Dendrinos, University College Cork
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Jonathan Hickman, University of Edinburgh
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Betsy Stovall, University of Wisconsin-Madison
About:
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.
Programme
| 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 | |
| Refreshments | ||
| 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 | |
| Refreshments | ||
| 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 | |
| Refreshments | ||
| Lillian Pierce , Duke University | Counterexamples disproving pointwise convergence for solutions of dispersive PDE’s | |
| Refreshments | ||
| 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 | |
| Refreshments | ||
| 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 | |
| Refreshments | ||
| 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 | |
| Refreshments | ||
| 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 | |
| Refreshments | ||
| 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 |
