Some News from a Seminar in Cambridge

On an old problems of Erdős

(h/t Michael Simkin and Nati Linial)

Here is a somewhat mysterious announcement for a combinatorics seminar lecture at Cambridge.

Which old problems of Erdős are we talking about? Here is a picture from the seminar itself.

 

Stay tuned (or try to test your intuition or guess in the comment section.)

Nothing yet here.
The paper is now on the arXiv.

An exponential improvement for diagonal Ramsey

Marcelo Campos, Simon Griffiths, Robert Morris, and Julian Sahasrabudhe

The Ramsey number is the minimum such that every red-blue colouring of the edges of the complete graph on vertices contains a monochromatic copy of . We prove that

for some constant . This is the first exponential improvement over the upper bound of Erdős and Szekeres, proved in 1935.