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Over the last decade the international research landscape in harmonic analysis has seen a dramatic and unexpected broadening of its connectivity within mathematics. The emergence of surprising new approaches to longstanding problems at the heart of the subject has led to many high-profile breakthroughs across mathematics. Many of these new developments can be traced back to the foundational contributions of Tony Carbery. The purpose of the proposed conference was to honour Tony Carbery by bringing together many of the key drivers of research in harmonic analysis at these important interfaces, at a time when international interest is at a peak.

This conference focused attention on aspects of harmonic analysis lying at the forefront of research in pure mathematics. Developments in just the last five years have transformed the profile of modern harmonic analysis, drawing attention from many communities, from the more classical dispersive PDEs and analytic number theory, to the more surprising algebraic geometry and topology.

The surge in pace of progress in harmonic analysis has exposed a wide variety of new and unexpected methodologies and applications, and the exploitation of many of these is still in its infancy. This workshop capitalised on this by drawing together research leaders in harmonic analysis at its interfaces across mathematics.