
Recent Posts
Archives
 August 2021 (1)
 March 2021 (2)
 November 2020 (1)
 October 2020 (1)
 September 2020 (3)
 August 2020 (2)
 January 2020 (2)
 December 2019 (1)
 September 2019 (1)
 July 2019 (1)
 May 2019 (1)
 September 2018 (1)
 April 2018 (1)
 March 2018 (1)
 November 2017 (2)
 August 2017 (2)
 July 2017 (1)
 April 2017 (2)
 September 2016 (1)
 July 2016 (1)
 May 2016 (2)
 December 2015 (1)
 October 2015 (1)
 August 2015 (2)
 June 2015 (1)
 May 2015 (1)
 April 2015 (1)
 March 2015 (4)
 January 2015 (1)
 September 2014 (3)
 August 2014 (1)
 July 2012 (3)
Categories
 Coding Theory (2)
 Combinatorics (38)
 Extremal Combinatorics (18)
 Ramsey Theory (7)
 Spectral Graph Theory (6)
 Conferences (1)
 Finite Geometry (28)
 Incidence Geometry (13)
 Job openings (1)
 Number Theory (1)
 Polynomial Method (15)
 Real Analysis (1)
 References (1)
 Research Diary (1)
 Uncategorized (2)
Blogs I Follow
 I Can't Believe It's Not Random!
 Random Permutations
 What's new
 Manu S Pillai
 cgroenland.wordpress.com/
 Radimentary
 Cosmin Pohoata
 Sleepless in Seattle
 Bloag
 Jagriti is professoring
 Math3ma
 Aparajita's blog
 The Intrepid Mathematician
 Ratio Bound – A Combinatorics Blog
 all the women
 ellipticnews
 Becoming My Better Self
 Points And Lines
 Some Plane Truths
 Gentzen translated
 E. Kowalski's blog
 Quomodocumque
 Short, Fat Matrices
 Combinatorics and more
 Yufei Zhao
 Abhishek Khetan
 urduwallahs
 Gaurish4Math
 Jerusalem Combinatorics Seminar
 Personal Blog
Category 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
Covering the binary hypercube
A finite grid is a set , where is a field and each is a finite subset of . The minimum number of hyperplanes required to cover can easily be shown to be , with the hyperplanes defined by , … 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
Leave a comment
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
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