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A generalization of the off-diagonal Ramsey numbers

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The Ramsey number R(s,t) stands for the smallest positive integer N such that whenever the edges of the complete graph on N vertices are 2-coloured with red and blue, then there is a red clique on s vertices or a blue clique on t vertices. In this talk, I will review the known results about this function, mentioning some famous open problems. I will also talk about how random graphs can be used to prove lower bounds on R(s,t). Then I will present a generalisation of this function and state a recent result of Gowers and myself, which is based on an unusual random graph construction.`

This talk is part of the Trinity Mathematical Society series.

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