[DMO] Sam Mattheus: Good lower bounds for off-diagonal Ramsey numbers from explicit constructions over finite fields

25 april 2024 16:00 t/m 17:00 - Locatie: EEMCS Lecture Hall Pi, 36.HB.01.580, | Zet in mijn agenda

We will present a recent approach, due to Mubayi and Verstraete, for lower bounds on off-diagonal Ramsey numbers. This approach, unlike previous results, has a strong non-probabilistic component. The main ingredient are certain explicit pseudorandom graphs which are often constructed from algebraic varieties over finite fields. This idea culminated in a recent breakthrough of Verstraete and myself in the determination of the asymptotic growth of the off-diagonal Ramsey number r(4,t), resolving a long-standing conjecture by Erdős. I will discuss some explicit constructions that appear in our and related work, and pose some open problems.