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Category Archives: Finite Geometry
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
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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The Cage Problem
I recently finished my research visit to UWA where I worked with John Bamberg and Gordon Royle on some finite geometrical problems related to cages. So this seems like the right time for me to write a blog post about … Continue reading
Posted in Combinatorics, Finite Geometry
Tagged cage, finite geometry, Gordon Royle, Graph Theory, John Bamberg, Moore graphs
2 Comments
Incidence Bounds and Interlacing Eigenvalues
The Szemerédi–Trotter theorem is one of the central results in discrete geometry which gives us a (tight) bound on the number of incidences, i.e., the number of pointline pairs with the point lying on the line, between finite sets of points and lines … Continue reading
Applications of AlonFuredi to finite geometry
In a previous post I discussed how the AlonFuredi theorem serves as a common generalisation of the results of Schwartz, DeMillo, Lipton and Zippel. Here I will show some nice applications of this theorem to finite geometry (reference: Section 6 of my … Continue reading
Posted in Combinatorics, Finite Geometry, Polynomial Method
Tagged AlonFuredi, blocking set, polynomials
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The EllenbergGijswijt bound on cap sets
Four days back Jordan Ellenberg posted the following on his blog: Briefly: it seems to me that the idea of the CrootLevPach paper I posted about yesterday can indeed be used to give a new bound on the size of subsets … Continue reading
Posted in Combinatorics, Finite Geometry, Polynomial Method
Tagged capset, Dion Gijswijt, Ernie Croot, Jordan Ellenberg, Peter Pach, Seva Lev
6 Comments