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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

Matrices coupled in a chain: I. Eigenvalue correlations

The general correlation function for the eigenvalues of p complex Hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.

Topological expansion for the 1-hermitian matrix model correlation functions

- B. Eynard
- Mathematics, Physics
- 1 November 2004

We rewrite the loop equations of the hermitian matrix model, in a way which involves no derivative with respect to the potential, we compute all the correlation functions, to all orders in the… Expand

Invariants of spectral curves and intersection theory of moduli spaces of complex curves

- B. Eynard
- Mathematics
- 13 October 2011

To any spectral curve S, we associate a topological class {\Lambda}(S) in a moduli space M^b_{g,n} of "b-colored" stable Riemann surfaces of given topology (genus g, n boundaries), whose integral… Expand

Torus Knots and Mirror Symmetry

We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants.… Expand

Hermitian matrix model free energy: Feynman graph technique for all genera

- L. Chekhov, B. Eynard
- Mathematics
- 13 April 2005

We present the diagrammatic technique for calculating the free energy of the Hermitian one-matrix model to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans… Expand

Matrix eigenvalue model: Feynman graph technique for all genera

- L. Chekhov, B. Eynard
- Mathematics
- 6 April 2006

We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power β by the Vandermonde determinant) to all orders of 1/N expansion… Expand

Breakdown of universality in multi-cut matrix models

We solve the puzzle of the disagreement between orthogonal polynomials methods and mean-field calculations for random N×N matrices with a disconnected eigenvalue support. We show that the difference… 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

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