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Explore recent advancements in the Erdos-Hajnal Conjecture through this illuminating lecture by Professor Alexander Scott of the University of Oxford. Delve into the world of extremal and probabilistic combinatorics, structural graph theory, and related areas of probability and computer science as Scott, an invited speaker at the 2022 International Congress of Mathematicians, shares his expertise. Gain insights into this longstanding mathematical problem and its implications in the field. The talk, lasting just over an hour, offers a comprehensive look at the current state of research on this important conjecture, drawing from Scott's extensive background in mathematics from Cambridge University and his current position at Oxford.