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Explore advanced concepts in extremal graph theory through this 54-minute lecture from the IAS/PCMI Park City Mathematics Institute. Delve into the extremal number ex(n, H), which represents the maximum number of edges in an H-free graph with n vertices, focusing particularly on the challenging case of bipartite graphs H where many open questions remain. Examine recent progress made in understanding extremal functions for bipartite graphs, building upon the well-established theory for non-bipartite cases. Learn from David Conlon of Caltech as he presents sophisticated mathematical techniques and current research developments in this central area of discrete mathematics. Access accompanying lecture notes and problem sets to reinforce your understanding of extremal combinatorics concepts. Gain insights into how extremal graph theory connects with other mathematical fields including analysis, geometry, number theory, statistical physics, and theoretical computer science as part of the broader PCMI 2025 program on Probabilistic and Extremal Combinatorics.
