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Tag 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
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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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
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Generalized hexagons containing a subhexagon
I have recently uploaded a joint paper with Bart, “On generalized hexagons of order and containing a subhexagon”,on arXiv and submitted it for publication. In this work we extend the results of my first paper, which I discussed here, by proving the following: … Continue reading
A timeline of the polynomial method upto combinatorial nullstellensatz
Over the past 3040 years, the socalled polynomial method has developed into a powerful tool in combinatorics and (additive) number theory. There has been a lot of recent interest in it after Dvir’s paper on the Kakeya conjecture, where he … Continue reading
Posted in Combinatorics, Finite Geometry, Polynomial Method
Tagged combinatorics, finite fields, finite geometry, polynomials
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