Algebraic methods in random matrices and enumerative geometry

Details Algebraic methods in random matrices and enumerative geometry Algebraic methods in random matrices and enumerative geometry

2008-11-21

arxiv.org/abs/0811.3531v1

Physics

Mathematical Physics

review article, Latex, 139 pages, many figures

Scientific paper

We review the method of symplectic invariants recently introduced to solve matrix models loop equations, and further extended beyond the context of matrix models. For any given spectral curve, one defined a sequence of differential forms, and a sequence of complex numbers Fg . We recall the definition of the invariants Fg, and we explain their main properties, in particular symplectic invariance, integrability, modularity,... Then, we give several example of applications, in particular matrix models, enumeration of discrete surfaces (maps), algebraic geometry and topological strings, non-intersecting brownian motions,...

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