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.

Ramsey numbers from pseudorandom graphs

Posted on September 30, 2019

One of the foundational results in modern combinatorics is Ramsey’s theorem which states that for every positive integers there exists a constant such that for all , every -coloring of edges of the complete graph has a monochromatic copy of … Continue reading →

Posted in Combinatorics, Extremal Combinatorics | Tagged , , , , , , | Leave a comment

Spectral proofs of theorems on the boolean hypercube

Posted on July 27, 2019

In a recent breakthrough Hao Huang proved the sensitivity conjecture, that had remained open for past 30 years despite some serious effort from various computer scientists and mathematicians. The proof can be described in a single tweet (if you have … Continue reading →

Posted in Combinatorics, Extremal Combinatorics, Spectral Graph Theory | Tagged , , , , , , , | 5 Comments

Pseudorandom clique-free graphs

Posted on May 15, 2019

Pseudorandom graphs are graphs that in some way behaves like a random graph with the same edge density. One way in which this happens is as follows. In the random graph , with , a direct application of Chernoff bound … Continue reading →

Posted in Combinatorics, Extremal Combinatorics, Spectral Graph Theory | Tagged , , | 2 Comments

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 , , , , , , , | 1 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