Richard M. Karp Distinguished Lecture — On Some Optimization Problems Involving a Large Number of Matrices

The past few years have witnessed an increased momentum in efforts to formulate optimal transportation problems in non commutative settings. These studies were motivated by finding appropriate metrics for equations in quantum mechanics or problems in quantum game theory. In this talk, we briefly survey some usefulness of the classical optimal transport theory and then switch to another transport problem introduced by Biane and Voiculescu in 2001. We state a duality result and comment on limits of systems of m–tuples of n×n matrices, as n tends to infinity. (This talk is based on a joint work with D. Jekel, K. Nam and D. Shlyakhtenko).

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