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Ramsey theory: searching for order in chaos

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  • UserRob Morris (IMPA Rio)
  • ClockThursday 02 May 2024, 16:00-17:00
  • HouseMR2, CMS.

If you have a question about this talk, please contact HoD Secretary, DPMMS.

In many different areas of mathematics (such as number theory, discrete geometry and combinatorics), one is often presented with a large “unstructured” object, and asked to find a smaller “structured” object inside it. One of the earliest and most influential examples of this phenomenon was the theorem of Ramsey, proved in 1930, which states that if n = n(k) is large enough, then in any red-blue colouring of the edges of the complete graph on n vertices, there exists a monochromatic clique on k vertices. In this talk I will discuss some of the questions, ideas, and new techniques that were inspired by this theorem, and mention some recent progress on one of the central problems in the area: bounding the so-called “diagonal” Ramsey numbers.

Based on joint work with Marcelo Campos, Simon Griffiths and Julian Sahasrabudhe.

A wine reception in the Central Core will follow the lecture

This talk is part of the Mordell Lectures series.

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