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Extremal Combinatorics
12 units

Classical problems and results in extremal combinatorics including the Turán and Zarankiewicz problems, the Erdős-Stone theorem and the Erd\H{o}os-Simonovits stability theorem. Extremal set theory including the Erdős-Rado sunflower lemma and variations, VC-dimension, and Kneser's conjecture. The Szemeredi regularity lemma. Algebraic methods including finite field constructions and eigenvalues and expansion properties of graphs. Shannon capacity of graphs. Chromatic number of Rn and Borsuk's conjecture. Graph decomposition including Graham-Pollack and Baranyai's theorem.