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Anurag's Math Blog

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Postdoc position in finite geometry and Ramsey theory

We are advertising a 3 year postdoctoral position at the University of Western Australia to work at the interface of finite geometry and Ramsey theory. The project is led by John Bamberg at UWA, Sam Mattheus at Vrije Universiteit Brussel, Continue reading

Tight bounds on off-diagonal Ramsey numbers

One of the oldest open problem in Ramsey theory has been solved. We now know the asymptotics of Ramsey numbers , for any fixed , up-to log factors. Last month, Domagoj Bradač showed that for any fixed and (where the Continue reading

Finite geometry paves the way for another Ramsey breakthrough

A sensational Ramsey breakthrough by Domagoj Bradač

Small complete cap sets

The following post is (partly) based on discussions with Dion Gijswijt and Ananth Ravi from September 2025. The famous cap set problem has attracted the attention of various mathematicians from different areas over the last few decades. It asks for Continue reading

Large induced matchings and minimal blocking sets using parabolas

In this post, I will discuss a recent breakthrough of Hunter, Pohoata, Verstraete and Zhang on an old problem in finite geometry, which also has interesting consequences outside this area. For example, it improves constructions in a minimal distance problem Continue reading

PhD and postdoc positions in Finite Geometry

I am hiring people on my NWO Vidi project. There is one PhD position (4 years) and one postdoc position (2 years) that you can apply for if you are interested. Use the following links to get more information and Continue reading

Coloring projective spaces and Ramsey theory

What is the minimum number of colors needed to color the points of the Fano plane such that there is no monochromatic line? It is a nice exercise to prove that two colors do not suffice. This fact has been Continue reading

Circular Sorting

How many swaps do you need to sort objects on a circle in clockwise order? This fairly simple and natural question quickly leads to some deep mathematics that I would like share. Let s start with an example for : After Continue reading

Constructing blocking sets using expander graphs and hypergraphs

Blocking sets are one of the central topics in finite geometry, which was originally introduced in the context of game theory under the name of `blocking coalitions : On Finite Projective Games. I first learned about them during my Ph.D. as Continue reading

The Rank-Ramsey problem

The Ramsey number is the smallest such that every graph on vertices either contains a clique of size or an independent set of size . Ramsey s theorem implies that these numbers always exist, and determining them (precisely or asymptotically) has Continue reading