Tag Archives: finite geometry

Ryser’s conjecture

Posted on September 20, 2018 by

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 by

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

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