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Explore a groundbreaking solution to Erdős and Hajnal's odd cycle problem in this hour-long lecture by Richard Montgomery, Associate Professor at the University of Warwick. Delve into the world of extremal and probabilistic combinatorics as Montgomery, a renowned mathematician and recipient of the European Prize in Combinatorics, presents his research findings. Learn about the intricacies of this long-standing mathematical challenge and gain insights into the innovative approaches used to tackle it. Suitable for advanced mathematics students and researchers interested in combinatorics and graph theory.