Tag Archives: finite geometry

Introduction to polynomial method

Posted on November 25, 2017 by

(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

What I have learned in finite geometry

Posted on August 13, 2017 by

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 by

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 Cage Problem

Posted on April 14, 2017 by

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 by

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

Generalized hexagons containing a subhexagon

Posted on July 5, 2016 by

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

A timeline of the polynomial method up-to combinatorial nullstellensatz

Posted on August 27, 2015 by

Over the past 30-40 years, the so-called polynomial method has developed into a powerful tool in combinatorics and (additive) number theory. There has been a lot of recent interest in it after Dvir’s  paper on the Kakeya conjecture, where he … Continue reading →

Posted in Combinatorics, Finite Geometry, Polynomial Method | Tagged , , , | 1 Comment