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Explore advanced concepts in Ramsey theory on graphs through this third lecture in a comprehensive series presented by Julian Sahasrabudhe from the University of Cambridge at the IAS/PCMI Park City Mathematics Institute. Delve into fundamental methods in modern combinatorics by examining how Ramsey theory has inspired techniques used throughout combinatorics and beyond. Learn about the theoretical foundations and applications of Ramsey theory in graph contexts, building upon concepts from previous lectures in this specialized graduate-level series. Access accompanying lecture notes and problem sets to reinforce your understanding of the material. This lecture forms part of PCMI 2025's research program on Probabilistic and Extremal Combinatorics, organized by leading researchers from LSE, Stanford University, University of Waterloo, IMPA, and Tel Aviv University, focusing on the connections between extremal and probabilistic combinatorics with other mathematical fields including analysis, geometry, number theory, statistical physics, and theoretical computer science.
