
Color-avoiding Paths
Yuval Wigderson, a mathematician at ETH Zürich, presents new results on directed paths in edge-colored tournaments that avoid a fixed color, delivered as part of the Institute for Advanced Study's Computer Science and Discrete Mathematics Seminar. He opens with Rédei's nearly century-old theorem that every tournament contains a Hamiltonian directed path, then builds toward color-avoiding variants developed with Jacob Fox and Benny Sudakov. The talk traces surprising links between this extremal combinatorics question and geometric packing, error-correcting codes, k-majority tournaments, Ramsey theory for sequences, convex geometry, Hilbert's inequality, and hypergraph Turán problems. Wigderson works through these connections one by one, aiming to show how a narrow-looking question about tournament colorings threads through several distant areas of mathematics. The seminar runs just over an hour and assumes familiarity with graph theory and combinatorics, pitched at researchers and graduate students rather than newcomers.