Jonathan Hickman has received an EPSRC New Investigator grant for his project 'Algebraic Methods in Harmonic Analysis'. The Fourier transform is a fundamental tool across mathematics, the physical sciences and engineering. Despite its enormous importance over the past 200 years, basic questions remain about the behaviour of the Fourier transform when applied to different classes of functions, and when the integral (or sum) used to define the Fourier transform will converge. Harmonic analysis is a branch of mathematics which grapples with these problems.Harmonic analysis is undergoing nothing short of a revolution, fuelled in part by the discovery that many core questions have nascent algebraic structure. This has led to the development of novel algebraic methods which have transformed the field and have brought about resolutions of many longstanding conjectures. Nevertheless, many of the most important problems in harmonic analysis are far from fully understood. The broad goal of this proposal is to harness the power of newly available tools to make progress on central problems in harmonic analysis and to develop new connections between these methods and other areas of mathematics.Click here to visit Dr Johnathan Hickan's personal website Tags Analysis and Probability Staff success Publication date 22 Aug, 2024
