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Topological recursion in enumerative geometry and random matrices

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...

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Detalles Bibliográficos
Autores principales: Eynard, Bertrand, Orantin, Nicolas
Lenguaje:eng
Publicado: 2009
Materias:
Acceso en línea:https://dx.doi.org/10.1088/1751-8113/42/29/293001
http://cds.cern.ch/record/1269037
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author Eynard, Bertrand
Orantin, Nicolas
author_facet Eynard, Bertrand
Orantin, Nicolas
author_sort Eynard, Bertrand
collection CERN
description 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.
id cern-1269037
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2009
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spelling cern-12690372019-09-30T06:29:59Zdoi:10.1088/1751-8113/42/29/293001http://cds.cern.ch/record/1269037engEynard, BertrandOrantin, NicolasTopological recursion in enumerative geometry and random matricesParticle Physics - TheoryMathematical Physics and MathematicsWe 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.oai:cds.cern.ch:12690372009
spellingShingle Particle Physics - Theory
Mathematical Physics and Mathematics
Eynard, Bertrand
Orantin, Nicolas
Topological recursion in enumerative geometry and random matrices
title Topological recursion in enumerative geometry and random matrices
title_full Topological recursion in enumerative geometry and random matrices
title_fullStr Topological recursion in enumerative geometry and random matrices
title_full_unstemmed Topological recursion in enumerative geometry and random matrices
title_short Topological recursion in enumerative geometry and random matrices
title_sort topological recursion in enumerative geometry and random matrices
topic Particle Physics - Theory
Mathematical Physics and Mathematics
url https://dx.doi.org/10.1088/1751-8113/42/29/293001
http://cds.cern.ch/record/1269037
work_keys_str_mv AT eynardbertrand topologicalrecursioninenumerativegeometryandrandommatrices
AT orantinnicolas topologicalrecursioninenumerativegeometryandrandommatrices