Bertrand Eynard and Nicolas Orantin 2009 J. Phys. A: Math. Theor. 42 293001 doi:10.1088/1751-8113/42/29/293001
Topological recursion in enumerative geometry and random matrices
REVIEW ARTICLEBertrand Eynard1,2 and Nicolas Orantin3
Show affiliationsTOPICAL REVIEW
We review the method of symplectic invariants recently introduced to solve matrix models' loop equations in the so-called topological expansion, and further extended beyond the context of matrix models. For any given spectral curve, one defines a sequence of differential forms and a sequence of complex numbers Fg called symplectic invariants. We recall the definition of Fg's and we explain their main properties, in particular symplectic invariance, integrability, modularity, as well as their limits and their deformations. Then, we give several examples of applications, in particular matrix models, enumeration of discrete surfaces (maps), algebraic geometry and topological strings, and non-intersecting Brownian motions.
- PACS
- MSC
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81T30 String and superstring theories; other extended objects (e.g., branes) (See also 83E30)
- Subjects
- Dates
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Issue 29 (24 July 2009)
Received 24 November 2009
Published 3 July 2009
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Topological recursion in enumerative geometry and random matrices
Bertrand Eynard and Nicolas Orantin 2009 J. Phys. A: Math. Theor. 42 293001
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