incidence geometry

Jun 18

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...

science mathematics llm math research openai large language models combinatorics breakthrough ramsey theory domagoj bradač incidence geometry extremal problems finite geometry finite fields ramsey numbers

Dec 02 2025

Coloring projective spaces and Ramsey theory

Anurag Bishnoi

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 known at least since the 1956 paper of Richardson that introduced the notion of...

mathematics math combinatorics extremal combinatorics caps ramsey theory incidence geometry extremal problems chromatic number vector spaces sum-free sets ramsey blocking set finite geometry finite fields ramsey numbers