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.

Ryser’s conjecture

Posted on September 20, 2018

I am on a research visit in Rome, working with Valentina Pepe, and our joint paper on Ryser’s conjecture is on arXiv now. So this seems like the right time to talk about the conjecture and the problems related to … Continue reading →

Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry | Tagged , , , , , , , , | 1 Comment

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