Mathematics Colloquium: Szemerédi’s theorem and additive combinatorics | Timothy Gowers

Описание: Online Mathematics colloquium by Professor Timothy Gowers (University of Cambridge), held on 20 May 2021.

Abstract: Additive combinatorics is a thriving field of mathematics that has come into existence in the last thirty years or so, though with many roots in older fields. One result that has stimulated many of the developments in the field is Szemerédi’s theorem, which states that every dense set of integers contains arbitrarily long arithmetic progressions. I shall try to explain what additive combinatorics is, and how it is that one theorem has come to have such a wide influence.

Bio: Timothy Gowers was born in 1963 into a family of musicians. Though music was important for him too, he settled on mathematics, studying at Cambridge University as an undergraduate and PhD student, where he was supervised by Béla Bollobás. He became a research fellow at Trinity College, then a lecturer at University College London, before returning to Cambridge in 1995, first as a lecturer, and then from 1998 as the Rouse Ball Professor of Mathematics. From 2009 to 2020 he was a Royal Society Research Professor, and in 2020 he became a professor at the Collège de France, while remaining a fellow of Trinity College and retaining an affiliation to Cambridge University. In 1998 he was awarded a Fields Medal for his work in functional analysis and combinatorics, and in 2012 he was knighted for services to mathematics. He is the author of Mathematics, A Very Short Introduction, and the main editor of The Princeton Companion to Mathematics.