Category Archives: Finite Geometry

An introduction to finite geometries with emphasis on its connection with graph theory, coding theory and group theory. I’ll be proving some elementary but really interesting results. I am grateful to Prof. Bhaskar Bagchi for introducing this beautiful field to me.

Wenger graphs

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

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What I have learned in finite geometry

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

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The cage problem and generalized polygons (part 1)

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

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The Cage Problem

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

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Expander Mixing Lemma in Finite Geometry

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

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Incidence Bounds and Interlacing Eigenvalues

The Szemerédi–Trotter theorem is one of the central results in discrete geometry which gives us a (tight) bound on the number of incidences, i.e., the number of point-line pairs with the point lying on the line, between finite sets of points and lines … Continue reading

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Applications of Alon-Furedi to finite geometry

In a previous post I discussed how the Alon-Furedi theorem serves as a common generalisation of the results of Schwartz, DeMillo, Lipton and Zippel. Here I will show some nice applications of this theorem to finite geometry (reference: Section 6 of my … Continue reading

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