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.

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