Author Archives: Anurag Bishnoi

About Anurag Bishnoi

Currently a maths PhD student at Ghent University working in the Incidence Geometry research group. I am broadly interested in combinatorics, finite geometry and group theory.

What I have learned in finite geometry

Posted on August 13, 2017

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 , , , , , , | Leave a comment

The cage problem and generalized polygons (part 1)

Posted on August 9, 2017

This post is a continuation of my previous post on the cage problem. Just to recall the main problem, for any given integers and , we want to find the least number of vertices in a simple undirected graph which … Continue reading →

Posted in Combinatorics, Finite Geometry, Incidence Geometry, Spectral Graph Theory, Uncategorized | Tagged , , , , | Leave a comment

The coefficient formula and Chevalley-Warning

Posted on July 17, 2017

We discuss the new simultaneous generalization of Chevalley-Warning and Morlaye’s result on polynomial equations over finite fields obtained by Pete Clark. Continue reading →

Posted in Number Theory, Polynomial Method | Tagged , , , , , , | 2 Comments

The Cage Problem

Posted on April 14, 2017

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 , , , , , | 2 Comments

Expander Mixing Lemma in Finite Geometry

Posted on April 2, 2017

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 →

Posted in Combinatorics, Finite Geometry, Incidence Geometry, Spectral Graph Theory | Tagged , , , , | 2 Comments

Incidence Bounds and Interlacing Eigenvalues

Posted on September 26, 2016

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 point-line pairs with the point lying on the line, between finite sets of points and lines … Continue reading →

Posted in Combinatorics, Finite Geometry, Incidence Geometry, Spectral Graph Theory | Tagged , , , , , , | 3 Comments

Generalized hexagons containing a subhexagon

Posted on July 5, 2016

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 →

Posted in Incidence Geometry | Tagged , , , | Leave a comment