Ramsey theory on homogeneous structures

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• Natasha Dobrinen (Denver)
• Thursday 17 February 2022, 14:30-15:30
• MR12.

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Ever since Ramsey proved his seminal theorem for colorings of finite sets of natural numbers, a question of interest has been the following: Which infinite structures carry analogues of the Infinite Ramsey Theorem? We will survey results and methods, beginning with Sierpinski’s unavoidable 2-coloring of pairs of rationals in the 1930’s through exact results on the Rado graph due to Laflamme, Sauer, and Vuksanovic in 2006. Then we will discuss new methods applicable to Ramsey theory on the triangle-free Henson graph, begun in 2015 while the speaker was visiting the INI , and survey recent extensions to other homogeneous structures with forbidden irreducible substructures.

This talk is part of the Combinatorics Seminar series.

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