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Explore recent advancements in Ramsey Theory through this 54-minute lecture by Jacques Verstraete at BIMSA. Delve into the Ramsey number r(s,t) and its significance in edge coloring of complete graphs. Examine the long-standing Erdős conjecture regarding the order of magnitude of r(s,t) as t approaches infinity. Discover new techniques involving pseudorandom graphs as effective Ramsey graphs, incorporating methods from geometry, algebra, probability, and combinatorics. Learn about the proof of Erdős' conjecture for r(4,t) and other novel constructions in Ramsey theory. Gain insights into this century-old field of study and its ongoing developments.
