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.

Wenger graphs

Posted on April 28, 2018

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 →

Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry | Tagged , , , , , , , | Leave a comment

The footprint bound

Posted on March 25, 2018

Studying the set of common zeros of systems of polynomial equations is a fundamental problem in algebra and geometry. In this post we will look at estimating the cardinality of the set of common zeros, when we already know that … Continue reading →

Posted in Coding Theory, Combinatorics, Polynomial Method | Tagged , , , , , , , | Leave a comment

Introduction to polynomial method

Posted on November 25, 2017

(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 , , , , | 2 Comments

On a famous pigeonhole problem

Posted on November 2, 2017

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

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, Extremal Combinatorics, Finite Geometry, Incidence Geometry, Spectral Graph Theory | 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