Description
Talk 1:
Speaker: Julian Sahasrabudhe (Cambridge)
Title: The r-colour diagonal Ramsey numbers
Abstract: In this talk I will discuss some of the ideas behind the recent improvement to the upper bounds on the diagonal multi-colour Ramsey numbers. Perhaps interestingly, a key new idea comes from geometric intutition.
This is based on joint work with Balister, Bollobás, Campos, Griffiths, Hurley, Morris and Tiba.
Talk 2:
Speaker: Marcelo Campos (IMPA)
Title: A new lower bound for the Ramsey numbers R(3,k)
Abstract: In this talk I will discuss a new lower bound for the off-diagonal Ramsey numbers R(3,k). For this, we develop a version of the triangle-free process that is significantly easier to analyse than the original process. We then 'seed' this process with a carefully chosen graph and show that it results in a denser graph that is still sufficiently pseudo-random to have small independence number.
This is based on joint work with Matthew Jenssen, Marcus Michelen and Julian Sahasrabudhe