Monthly Archives: March 2015

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

Posted in Finite Geometry, Polynomial Method | Tagged , , | 1 Comment

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

Posted in Combinatorics, Finite Geometry | Tagged , , | 2 Comments

My first publication

Today, my supervisor Prof. Bart De Bruyn got the acceptance email from the editor of Annals of Combinatorics for our joint paper “On semi-finite hexagons of order containing a subhexagon” which we had submitted in July 2014. Both the referee reports … Continue reading

Posted in Finite Geometry | Tagged , , | 6 Comments

Two proofs of the Schwartz-Zippel lemma

The fact that a univariate polynomial over a field of degree has at most zeroes is well known. It follows from the so called Factor theorem, if and only if . But what about a polynomial in -variables, , where … Continue reading

Posted in Finite Geometry, Polynomial Method | Tagged , , | 8 Comments