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Random matrices and the Rogers-Ramanujan identities


Speaker: Jason Fulman, Mathematics, Stanford
Location: 693 Kerr
Start time: Tue, Feb 1 2000, 4:10PM

Motivated by the theory of random matrices chosen from the finite classical groups, we define probability measures on the set of all partitions of all natural numbers. Using relations with symmetric function theory, several purely probabilistic ways of understanding these measures are given. One such method uses Markov chains and gives a simple proof of the celebrated Rogers-Ramanujan identities, suggesting generalizations to quivers. If time permits, we will describe progress related to the combinatorially harder question of the Jordan form of random upper triangular matrices over a finite field.