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Explore advanced techniques in modern combinatorics through this graduate-level lecture focusing on Ramsey theory in the context of graphs. Learn fundamental methods that have influenced combinatorics and related fields, as part of a comprehensive course examining how this single topic has inspired numerous techniques used throughout mathematics. Discover the connections between extremal and probabilistic combinatorics while studying discrete structures and their restrictions. Benefit from expert instruction by Julian Sahasrabudhe from the University of Cambridge as part of the PCMI 2025 Graduate Summer School program on Probabilistic and Extremal Combinatorics, which emphasizes the strong connections between these fields and other areas of mathematics including analysis, geometry, number theory, statistical physics, and theoretical computer science.
