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Explore advanced topics in probabilistic and extremal combinatorics through this comprehensive graduate-level program from the Park City Mathematics Institute. Delve into two central branches of discrete mathematics: extremal combinatorics, which studies the maximum or minimum size of discrete structures under given constraints, and probabilistic combinatorics, which investigates random combinatorial objects using probability theory and combinatorial methods. Master key concepts through nine mini-course series covering asymptotic enumeration via graph containers and entropy, arithmetic Ramsey theory, enumeration of regular graphs, sunflowers to thresholds, sublinear expander graphs, Ramsey theory on graphs, statistical physics approaches to asymptotic enumeration and large deviations in random graphs, intersecting families, and extremal graph theory. Learn from leading researchers including Jinyoung Park, Sarah Peluse, Anita Liebenau, Shachar Lovett, Matija Bucić, Julian Sahasrabudhe, Will Perkins, Imre Leader, David Conlon, and Rob Morris. Discover connections between these fields and other mathematical areas such as analysis, geometry, number theory, statistical physics, and theoretical computer science. Gain insights into specialized topics including graph codes, machine learning applications to pure mathematics, topological aspects of knitting theory, and geometric problems in discrete mathematics through additional lectures by renowned mathematicians like Noga Alon, Jordan Ellenberg, Sabetta Matsumoto, Tadashi Tokieda, and János Pach.
