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Explore advanced mathematical research in this seminar lecture from the Institute for Advanced Study's Computer Science/Discrete Mathematics Seminar series. Delve into groundbreaking work on multicolour Ramsey numbers, where the speaker presents new upper bounds for the r-colour Ramsey number Rr(k) - the minimum number of vertices needed to guarantee a monochromatic copy of Kk in any r-colouring of a complete graph's edges. Learn about the proof that establishes Rr(k)≤e−δkrrk for fixed r≥2, representing the first exponential improvement over the classical 1935 Erdős-Szekeres upper bound for r≥3. Discover how this research provides an alternative, significantly shorter proof for the r=2 case, building on recent work by Campos, Griffiths, Morris and Sahasrabudhe. Gain insights into collaborative mathematical research involving prominent mathematicians including Paul Balister, Bela Bollobas, and others, as presented by Marius Tiba from King's College London in this comprehensive 86-minute academic presentation.
