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Algebraic methods in random matrices and enumerative geometry

Authors
  • Eynard, Bertrand
  • Orantin, Nicolas
Type
Preprint
Publication Date
Nov 21, 2008
Submission Date
Nov 21, 2008
Source
arXiv
License
Yellow
External links

Abstract

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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