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Tag Archives: finite geometry
A coding theoretic application of the AlonFüredi theorem
The AlonFüredi theorem is something that I have written a lot about in this blog. I spent a considerable amount of time on this theorem during my PhD. In fact, it’s generalisation that I obtained and it’s applications in finite … Continue reading
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
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
Ryser’s conjecture
I am on a research visit in Rome, working with Valentina Pepe, and our joint paper on Ryser’s conjecture is on arXiv now. So this seems like the right time to talk about the conjecture and the problems related to … 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
Introduction to polynomial method
(The following is a blogfriendly version of Chapter 7 of my PhD thesis, which is an introduction to the socalled polynomial method.) The polynomial method is an umbrella term for different techniques involving polynomials which have been used to solve … Continue reading
What I have learned in finite geometry
On September 2nd, 2014 I wrote a blog post titled learning finite geometry, in which I described how much I have learned in my first year of PhD and more importantly, the topics that I wish to learn while I … Continue reading
Posted in Combinatorics, Finite Geometry, Incidence Geometry, Research Diary
Tagged blocking set, combinatorics, finite geometry, learning, PhD, polar spaces, unitals
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