Tag Archives: finite geometry

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

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Expander Mixing Lemma in Finite Geometry

In this post I will discuss some nice applications of the expander mixing lemma in finite incidence geometry, including a new result that I have obtained recently. In many of the applications of the lemma in finite geometry, the graph is bipartite, and … Continue reading

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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

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A timeline of the polynomial method up-to combinatorial nullstellensatz

Over the past 30-40 years, the so-called 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

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Chevalley-Warning Theorem and Blocking Sets

The classical Chevalley-Warning theorem gives us a sufficient condition for a system of polynomial equations over a finite field to have common solutions. Affine blocking sets are sets of points in an affine geometry (aka affine space) that intersect every hyperplane. … Continue reading

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The Kakeya problem

The original Kakeya needle problem  is to  find the least amount of area required to continuously rotate a unit line segment in the (Euclidean) plane by a full rotation. Of course in a circle of diameter one we can continuously … Continue reading

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Point-Line 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

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