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In this special colloquium, Julian Sahasrabudhe will speak about his recent extraordinary breakthrough on the diagonal Ramsey problem, joint with Marcelo Campos, Simon Griffiths and Rob Morris. 

Julian is an assistant professor at the University of Cambridge, and winner of the European Prize in Combinatorics. Prior to his appointment at Cambridge, Julian was a Junior Research Fellow at Peterhouse, University of Cambridge (2017-2021). In 2017-2018, he visited Rob Morris at IMPA (Instituto Nacional de Matemática Pura e Aplicada) in Rio de Janerio, Brazil as a post-doc of excellence. He did his PhD under the supervision of Béla Bollobás at the University of Memphis.


Title: An exponential improvement for diagonal Ramsey

Abstract: Let R(k) be the kth diagonal Ramsey number: that is, the smallest n for which every 2-colouring of the edges of K_n contains a monochromatic K_k. In recent work with Marcelo Campos, Simon Griffiths and Rob Morris, the speaker showed that R(k) < (4-c)^k, for some absolute constant c>0. This is the first exponential improvement over the bound of Erdős and Szekeres, proved in 1935. In this talk I will discuss the proof.

The talk will be followed by tea & coffee in the Strand Building, room S-2.23. 

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