Author Archives: Anurag Bishnoi

About Anurag Bishnoi

A mathematician working at FU Berlin as a postdoc. I am broadly interested in combinatorics and finite geometry.

Introduction to polynomial method

(The following is a blog-friendly version of Chapter 7 of my PhD thesis, which is an introduction to the so-called polynomial method.) The polynomial method is an umbrella term for different techniques involving polynomials which have been used to solve … Continue reading

Posted in Combinatorics, Incidence Geometry, Polynomial Method | Tagged , , , , | Leave a comment

On a famous pigeonhole problem

After a short break from blogging, which involved moving from Ghent to Berlin, dealing with German bureaucracy, and learning how to make simple websites (the easiest bit), I am now back. I am working as a postdoc at the Free … Continue reading

Posted in Combinatorics, Extremal Combinatorics | Tagged , , , , | 5 Comments

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 , , , , , , | Leave a comment

The cage problem and generalized polygons (part 1)

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

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

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

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