Partitions, matrix models, and geometry
Seminar Room 1, Newton Institute
Sums of partitions with the Plancherel measure appear in various problems of statistical physics and mathematics (crystal growth, point processes, Gromov-Witten invariants). We rewrite such sums as matrix integrals, which allow to compute their large size expansion to all orders. The coefficients in the expansion are geometric objects called symplectic invariants of spectral curves. This makes a link between combinatorics of partitions, matrix models, algebraic geometry, integrability, quantum field theory and topological string theory.
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