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Category Archives: Ramsey Theory
A short video on Ramsey numbers
I was recently involved in making a 1 minute maths video for a contest organised by Veritasium. Here is the main requirement for the video We are looking for videos that clearly and creatively explain complex or counterintuitive concepts in … Continue reading
Posted in Combinatorics, Ramsey Theory
Tagged combinatorics, extremal problems, ramsey, ramsey numbers, Veritasium, Youtube
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Bilinear forms and diagonal Ramsey numbers
The recent breakthrough of Conlon and Ferber has shown us that algebraic methods can be used in combination with probabilistic methods to improve bounds on multicolour diagonal Ramsey numbers. This was already shown for the offdiagonal Ramsey numbers by Mubayi … Continue reading
Improved lower bounds for multicolour diagonal Ramsey numbers
Big news in combinatorics today: David Conlon and Asaf Ferber have posted a 4page preprint on arXiv that gives exponential improvements in the lower bounds on multicolour diagonal Ramsey numbers, when the number of colours is at least (also see … Continue reading
Heisenberg groups, irreducible cubics and minimal Ramsey
As I mentioned in a previous post, we recently improved the upper bound on a Ramsey parameter, in collaboration with John Bamberg and Thomas Lesgourgues. My favourite thing about this work is how it ends up using the properties of … Continue reading
Generalized polygons in extremal combinatorics
Jacques Tits invented generalized polygons to give a geometrical interpretation of the exceptional groups of Lie type. The prototype of these incidence geometries already appears in his 1956 paper, while they are axiomatically defined in his influential 1959 paper on … Continue reading
Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry, Ramsey Theory, Uncategorized
Tagged extremal problems, generalized polygons, generalized quadrangles, Graph Theory, hypergraphs, John Bamberg, ramsey, ramsey numbers, research, Thomas Lesgourgues, turan problems
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Minimal Ramsey problems
Thanks to Anita Liebenau, I have recently been introduced to some very interesting questions in Ramsey theory and I have been working on them for the past few months in collaboration with various people. In my recent joint work with … Continue reading
Bounds on Ramsey numbers from finite geometry
In an earlier post I talked about the work of Mubayi and Verstraete on determining the offdiagonal Ramsey numbers via certain optimal pseudorandom graphs, which are not yet known to exist except for the case of triangles. Beyond this conditional … Continue reading