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finite geometry

Tight bounds on off-diagonal Ramsey numbers

Anurag Bishnoi

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 term is hiding log factors), using a beautiful finite-geometric...

Small complete cap sets

Anurag Bishnoi

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 the largest possible size, , of a 3-term...

Large induced matchings and minimal blocking sets using parabolas

Anurag Bishnoi

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 in and it has been adapted by Ihringer...

Constructing blocking sets using expander graphs and hypergraphs

Anurag Bishnoi

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 a source of extremal problems that over the years as led...