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Tag Archives: generalized quadrangles
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
Wenger graphs
A central (and foundational) question in extremal graph theory is the forbidden subgraph problem of Turán, which asks for the largest number of edges in an vertex graph that does not contain any copy of a given graph as its … Continue reading
PointLine Geometries
Some notation: The set will be denoted by . For every set we have the set of all subsets of , also known as the power set, which we will denote by . This notation makes some sense if you … Continue reading
Posted in Combinatorics, Finite Geometry
Tagged combinatorics, finite geometry, generalized quadrangles
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