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Explore fundamental methods in modern combinatorics through this graduate-level lecture focusing on Ramsey theory in the context of graphs. Discover how this single topic has inspired numerous techniques used throughout combinatorics and beyond, as presented by Julian Sahasrabudhe from the University of Cambridge at the IAS/PCMI Park City Mathematics Institute. Learn about the connections between extremal and probabilistic combinatorics, two central branches of contemporary discrete mathematics that study how large or small discrete structures can be under certain restrictions and investigate random combinatorial objects using probability theory. Gain insights into how these fields connect with other areas of mathematics including analysis, geometry, number theory, statistical physics, and theoretical computer science. Access accompanying lecture notes and problem sets to deepen your understanding of the material presented in this comprehensive exploration of Ramsey theory's role in modern mathematical research.
