Rankin-Sneddon Lecture 2023: Fourier interpolation and the Weil representation
Prof Akshay Venkatesh FRS (Institute of Advanced Study, Princeton, NJ)
Thursday 23rd March, 2023 16:00-17:00
Abstract
In an exciting opportunity to hear about mathematics from a Fields’ medalist, Prof Akshay Venkatesh FRS (Institute of Advanced Study, Princeton, NJ) will give the upcoming Rankin-Sneddon Lecture, to which the School of Mathematics and Statistics is delighted to invite you.
The lecture, entitled Fourier interpolation and the Weil representation will be held on Thursday 23rd March 2023, 16:00 - 17:00 GMT in Lecture Theatre 116 of the Mathematics and Statistics Building, with a wine reception to follow at 17:00.
To attend in-person, please register at https://rankin-lecture-2023.eventbrite.co.uk
To attend online, please register at https://rankin-lecture-2023-online.eventbrite.co.uk
About the speaker
Professor Akshay Venkatesh FRS gained recognition in a broad range of areas of pure mathematics. He was awarded the Fields Medal, commonly described as the Nobel Prize of mathematics, in 2018 for “his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects.” He was also awarded the Ostrowski prize in 2018, the Infosys prize in 2017, the SASTRA Ramanujan prize in 2008, the Salem Prize in 2007 and held a Clay Math Research Fellowship in 2004-06, among others.
Abstract
Work of Segal and Shale around 1960 introduced to mathematics the remarkable "oscillator representation", a group of transformations of square integrable functions on the real line. This was motivated by structures arising in quantum mechanics; later, Weil related it to the classical theory of theta functions. I will give an introduction to the oscillator representation and give some examples illustrating how it arises naturally in mathematics and physics. I will then use it to give a new proof of a beautiful interpolation statement about Schwartz functions on the real line, discovered by Radchenko and Viazovska. This is joint work with Mathilde Gerbelli-Gauthier.
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