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## Invariants of algebraic curves and topological expansion

- B. Eynard, N. Orantin
- Mathematics
- 14 February 2007

For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties.… Expand

## Identification of the Givental Formula with the Spectral Curve Topological Recursion Procedure

- P. Dunin-Barkowski, N. Orantin, S. Shadrin, L. Spitz
- Mathematics
- 16 November 2012

We identify the Givental formula for the ancestor formal Gromov–Witten potential with a version of the topological recursion procedure for a collection of isolated local germs of the spectral curve.… Expand

## Algebraic methods in random matrices and enumerative geometry

- B. Eynard, N. Orantin
- Mathematics
- 21 November 2008

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… Expand

## Topological recursion in enumerative geometry and random matrices

- B. Eynard, N. Orantin
- Mathematics
- 24 July 2009

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… Expand

## Abstract loop equations, topological recursion, and applications

- G. Borot, B. Eynard, N. Orantin
- Mathematics
- 23 March 2013

We formulate a notion of abstract loop equations, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The… Expand

## Holomorphic anomaly and matrix models

- B. Eynard, M. Mariño, N. Orantin
- Mathematics
- 14 February 2007

The genus g free energies of matrix models can be promoted to modular invariant, non-holomorphic amplitudes which only depend on the geometry of the classical spectral curve. We show that these… Expand

## Free energy topological expansion for the 2-matrix model

- L. Chekhov, B. Eynard, N. Orantin
- Mathematics
- 1 March 2006

We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/N expansion of the… Expand

## The ABCD of topological recursion

- J. Andersen, G. Borot, L. Chekhov, N. Orantin
- Mathematics
- 9 March 2017

Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of math-ph/0702045, seeing it as a quantization of certain quadratic Lagrangians in $T^*V$ for some vector… Expand

## CFT and topological recursion

- I. Kostov, N. Orantin
- Mathematics
- 10 June 2010

We study the quasiclassical expansion associated with a complex curve. In a more specific context this is the 1/N expansion in U(N)-invariant matrix integrals. We compare two approaches, the CFT… Expand

## Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models

- B. Eynard, N. Orantin
- Mathematics
- 24 May 2007

We show that Mirzakhani's recursions for the volumes of moduli space of Riemann surfaces are a special case of random matrix loop equations, and therefore we confirm again that Kontsevitch's integral… Expand

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