B. Eynard

发表

Random matrices.

B. Eynard, Taro Kimura, S. Ribault, 2015, 1510.04430.

Matrices coupled in a chain: I. Eigenvalue correlations

M. L. Mehta, B. Eynard, M. Mehta, 1998 .

A Holomorphic and background independent partition function for matrix models and topological strings

B. Eynard, M. Mariño, 2008, 0810.4273.

Loop equations from differential systems

B. Eynard, O. Marchal, Raphael Belliard, 2016, 1602.01715.

Preprint : IPhT-16 / 007 , CRM-3352 Loop equations from differential systems

B. Eynard, O. Marchal, Raphael Belliard, 2016 .

Weighted Hurwitz numbers and topological recursion: An overview

B. Eynard, J. Harnad, A. Alexandrov, 2016, Journal of Mathematical Physics.

Counting Riemann Surfaces

B. Eynard, 2016 .

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

B. Eynard, L. Chekhov, 2005, hep-th/0504116.

Topological recursion in enumerative geometry and random matrices

B. Eynard, N. Orantin, 2009 .

N ov 2 00 9 SUPERMATRIX MODELS , LOOP EQUATIONS , AND DUALITY

B. Eynard, P. Desrosiers, 2021 .

Breakdown of universality in multi-cut matrix models

B. Eynard, F. David, G. Bonnet, 2000, cond-mat/0003324.

Algebraic methods in random matrices and enumerative geometry

B. Eynard, N. Orantin, 2008, 0811.3531.

All order asymptotic expansion of large partitions

B. Eynard, Bertrand Eynard, 2008, 0804.0381.

Matrices coupled in a chain: I. Eigenvalue correlations

M. L. Mehta, B. Eynard, M. Mehta, 1997, cond-mat/9710230.

Mirror of the refined topological vertex from a matrix model

B. Eynard, C. Kozçaz, 2011, 1107.5181.

Semiclassical Orthogonal Polynomials, Matrix Models and Isomonodromic Tau Functions

B. Eynard, J. Harnad, M. Bertola, 2004, nlin/0410043.

Double Scaling Limit in Random Matrix Models and a Nonlinear Hierarchy of Differential Equations

B. Eynard, P. Bleher, 2002, hep-th/0209087.

The PDEs of Biorthogonal Polynomials Arising in the Two-Matrix Model

B. Eynard, M. Bertola, 2003, nlin/0311033.

Large N asymptotics of orthogonal polynomials, from integrability to algebraic geometry

B. Eynard, 2005, math-ph/0503052.

Differential Systems for Biorthogonal Polynomials Appearing in 2-Matrix Models and the Associated Riemann–Hilbert Problem

B. Eynard, J. Harnad, M. Bertola, 2002, nlin/0208002.

Asymptotics of skew orthogonal polynomials

B. Eynard, Bertrand Eynard, 2000, cond-mat/0012046.

Partition functions for matrix models and isomonodromic tau functions

B. Eynard, J. Harnad, M. Bertola, 2002, nlin/0204054.

Think globally, compute locally

B. Eynard, V. Bouchard, 2012, 1211.2302.

Free energy topological expansion for the 2-matrix model

B. Eynard, N. Orantin, L. Chekhov, 2006, math-ph/0603003.

Topological expansion for the 1-hermitian matrix model correlation functions

B. Eynard, 2004 .

Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

J. Zuber, P. Francesco, B. Eynard, 2006, math-ph/0610049.

Master loop equations, free energy and correlations for the chain of matrices

B. Eynard, 2003, hep-th/0309036.

The Potts-q random matrix model: loop equations, critical exponents, and rational case

B. Eynard, G. Bonnet, 1999, hep-th/9906130.

Toward U ( N | M ) knot invariant from ABJM theory

B. Eynard, Taro Kimura, 2017 .

Toward $$\mathrm {U}(N|M)$$U(N|M) knot invariant from ABJM theory

B. Eynard, Taro Kimura, 2014, 1408.0010.

J Theory and Experiment Loop equations for the semiclassical 2-matrix model with hard edges B Eynard

B. Eynard, 2005 .

Exact solution of the O(n) model on a random lattice

B. Eynard, C. Kristjansen, 1995, hep-th/9506193.

Duality, Biorthogonal Polynomials¶and Multi-Matrix Models

B. Eynard, J. Harnad, M. Bertola, 2001, nlin/0108049.

Holomorphic anomaly and matrix models

B. Eynard, N. Orantin, M. Mariño, 2007, hep-th/0702110.

An iterative solution of the three-colour problem on a random lattice

B. Eynard, C. Kristjansen, 1997, cond-mat/9710199.

More on the exact solution of the O(n) model on a random lattice and an investigation of the case ∥n∥ > 2

B. Eynard, C. Kristjansen, 1995, hep-th/9512052.

A Matrix Model for the Topological String I: Deriving the Matrix Model

B. Eynard, Amir-Kian Kashani-Poor, Olivier Marchal, 2013, Annales Henri Poincaré.

Annales Henri Poincaré Torus Knots and Mirror Symmetry

B. Eynard, A. Brini, M. Mariño, 2017 .

Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices

B. Eynard, Bertrand Eynard, 1997, cond-mat/9707005.

Lectures on compact Riemann surfaces

B. Eynard, 2018 .

Lectures notes on compact Riemann surfaces

B. Eynard, 2018, 1805.06405.

A concise expression for the ODE's of orthogonal polynomials

B. Eynard, 2001, math-ph/0109018.

The O(n) model on a random surface: critical points and large-order behaviour

B. Eynard, J. Zinn-Justin, 1992, hep-th/9204082.

Weighted Hurwitz Numbers and Topological Recursion

B. Eynard, J. Harnad, A. Alexandrov, 2020, Communications in Mathematical Physics.

Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

B. Eynard, J. Harnad, A. Alexandrov, 2017, Communications in Mathematical Physics.

Correlation functions of eigenvalues of multi-matrix models, and the limit of a time-dependent matrix

B. Eynard, 1998, cond-mat/9801075.

Matrix eigenvalue model: Feynman graph technique for all genera

B. Eynard, L. Chekhov, 2006, math-ph/0604014.

Mixed correlation function and spectral curve for the 2-matrix model

B. Eynard, M. Bergère, 2006, math-ph/0605010.

Large order behaviour of 2D gravity coupled to D>1 matter

B. Eynard, J. Zinn-Justin, Jean Zinn-Justin, 1993, hep-th/9301004.

Planar maps, circle patterns and 2D gravity

B. Eynard, F. David, 2013, 1307.3123.

The sine-law gap probability, Painlev\'e 5, and asymptotic expansion by the topological recursion

B. Eynard, O. Marchal, M. Bergère, 2013, 1311.3217.

Topological expansion of the β-ensemble model and quantum algebraic geometry in the sectorwise approach

B. Eynard, O. Marchal, L. Chekhov, 2010, 1009.6007.

Large deviations of the maximal eigenvalue of random matrices

S. Majumdar, C'eline Nadal, B. Eynard, 2010, 1009.1945.

Topological expansion of the Bethe ansatz, and quantum algebraic geometry

B. Eynard, O. Marchal, L. Chekhov, 2009, 0911.1664.

Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry

B. Eynard, O. Marchal, 2008, 0809.3367.

Invariants of algebraic curves and topological expansion

B. Eynard, N. Orantin, B. Eynard, 2007, math-ph/0702045.

Loop equations for the semiclassical 2-matrix model with hard edges

B. Eynard, 2005, math-ph/0504002.

A Matrix Model for the Topological String II: The Spectral Curve and Mirror Geometry

B. Eynard, O. Marchal, A. Kashani-Poor, 2010, 1007.2194.

A Matrix Model for the Topological String I: Deriving the Matrix Model

B. Eynard, O. Marchal, A. Kashani-Poor, 2010, 1003.1737.

Root systems, spectral curves, and analysis of a Chern-Simons matrix model for Seifert fibered spaces

A. Weisse, B. Eynard, G. Borot, 2014, 1407.4500.

Torus Knots and Mirror Symmetry

B. Eynard, A. Brini, M. Mariño, 2011, 1105.2012.

Workshop: Low-dimensional Topology and Number Theory Table of Contents

Paul E. Gunnells, Jessica S. Purcell, Adam S. Sikora, 2012 .

All-order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials

B. Eynard, G. Borot, 2012, 1205.2261.

Abstract loop equations, topological recursion, and applications

B. Eynard, N. Orantin, G. Borot, 2013, 1303.5808.

From topological recursion to wave functions and PDEs quantizing hyperelliptic curves

B. Eynard, Elba Garcia-Failde, 2019, 1911.07795.

From the quantum geometry of Fuchsian systems to conformal blocks of W-algebras

B. Eynard, Raphael Belliard, 2019, 1907.10543.

Reconstructing WKB from topological recursion

B. Eynard, V. Bouchard, 2016, 1606.04498.

Geometry of Spectral Curves and All Order Dispersive Integrable System

B. Eynard, G. Borot, 2011, 1110.4936.

Combinatorial expression of the fundamental second kind differential on an algebraic curve

B. Eynard, 2018, Annales de l'Institut Henri Poincaré D.

The Geometry of integrable systems. Tau functions and homology of Spectral curves. Perturbative definition

B. Eynard, 2017, 1706.04938.

Rational Differential Systems, Loop Equations, and Application to the qth Reductions of KP

B. Eynard, G. Borot, M. Bergère, 2013, 1312.4237.

Determinantal formulae and loop equations

B. Eynard, M. Bergère, 2009, 0901.3273.

Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence

B. Eynard, 2008, 0802.1788.

Topological expansion for the 1-hermitian matrix model correlation functions

B. Eynard, B. Eynard, 2004 .

Computation of Open Gromov–Witten Invariants for Toric Calabi–Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture

B. Eynard, N. Orantin, 2012, 1205.1103.

A matrix model for simple Hurwitz numbers, and topological recursion

B. Eynard, B. Eynard, G. Borot, 2009, 0906.1206.

Universal scaling limits of matrix models, and $(p,q)$ Liouville gravity

B. Eynard, M. Bergère, 2009, 0909.0854.

The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers

B. Eynard, M. Mulase, B. Safnuk, 2009, 0907.5224.

A short overview of the "Topological recursion"

B. Eynard, 2014, 1412.3286.

The geometry of Casimir W-algebras

B. Eynard, S. Ribault, Raphael Belliard, 2017, SciPost Physics.

Counting Surfaces: CRM Aisenstadt Chair lectures

Bertrand Eynard, B. Eynard, 2016 .

Integrability of $\mathcal W({\mathfrak{sl}_d})$-symmetric Toda conformal field theories I : Quantum geometry

B. Eynard, Raphael Belliard, 2018, 1801.03433.

Integrability of W(sld)-symmetric Toda conformal field theories I : Quantum geometry

B. Eynard, Raphael Belliard, 2018 .

Loop Equations from Differential Systems on Curves

B. Eynard, Raphael Belliard, O. Marchal, 2017, Annales Henri Poincaré.

Integrable Differential Systems of Topological Type and Reconstruction by the Topological Recursion

B. Eynard, Raphael Belliard, O. Marchal, 2017, Annales Henri Poincaré.

Integrable Differential Systems of Topological Type and Reconstruction by the Topological Recursion

B. Eynard, O. Marchal, Raphaël Belliard, 2016, 1610.00496.

Lax matrix solution of c = 1 conformal field theory

B. Eynard, S. Ribault, 2013, 1307.4865.

Seiberg-Witten equations and non-commutative spectral curves in Liouville theory

B. Eynard, S. Ribault, L. Chekhov, 2012, 1209.3984.

Loop equations and topological recursion for the arbitrary-β two-matrix model

B. Eynard, O. Marchal, M. Bergère, 2011, 1106.0332.

Formal Matrix Integrals and Combinatorics of Maps

Bertrand Eynard, B. Eynard, 2006, math-ph/0611087.

Integrability of $\mathcal W(\widehat{\mathfrak{sl}_d})$-symmetric Toda conformal field theories I : Quantum geometry

B. Eynard, Raphael Belliard, 2018 .

About the x-y symmetry of the F_g algebraic invariants

B. Eynard, N. Orantin, 2013, 1311.4993.

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

B. Eynard, N. Orantin, 2007, 0705.3600.

Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants

B. Eynard, N. Orantin, 2007, 0705.0958.

Weighted Hurwitz Numbers and Topological Recursion

B. Eynard, J. Harnad, A. Alexandrov, 2018 .

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

B. Eynard, 2011, 1110.2949.

Intersection numbers of spectral curves

B. Eynard, 2011, 1104.0176.

Recursion Between Mumford Volumes of Moduli Spaces

B. Eynard, 2007, 0706.4403.

Topological Recursion, Airy structures in the space of cycles

B. Eynard, 2019, 1912.03339.

Quantization of classical spectral curves via topological recursion

Elba Garcia-Failde, Olivier Marchal, Bertrand Eynard, 2021, 2106.04339.

Genus one contribution to free energy in Hermitian two-matrix model

B. Eynard, A. Kokotov, D. Korotkin, 2004 .

1/N2 Correction to Free Energy in Hermitian Two-Matrix Model

B. Eynard, A. Kokotov, D. Korotkin, 2004, hep-th/0401166.

Counting Large Maps

B. Eynard, 2016 .

Large N expansion of the 2-matrix model, multicut case

B. Eynard, B. Eynard, 2003, math-ph/0307052.

BMN Correlators by Loop Equations

B. Eynard, C. Kristjansen, 2002, hep-th/0209244.

Correlators by Loop Equations

B. Eynard, 2022 .

A matrix model for plane partitions

Bertrand Eynard, B. Eynard, 2009, 0905.0535.

A Matrix model for plane partitions and TASEP

B. Eynard, 2009 .

A natural basis for intersection numbers

Bertrand Eynard, Danilo Lewa'nski, Adrien Ooms, 2021, 2108.00226.

A Dissociation of Attention, Executive Function and Reaction to Difficulty: Development of the MindPulse Test, a Novel Digital Neuropsychological Test for Precise Quantification of Perceptual-Motor Decision-Making Processes

B. Eynard, S. Granon, S. Suarez, 2021, Frontiers in Neuroscience.

Rational Differential Systems, Loop Equations, and Application to the qth Reductions of KP

B. Eynard, G. Borot, M. Bergère, 2015, Annales Henri Poincaré.

Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula

B. Eynard, N. Orantin, 2005, math-ph/0504058.

Solution of Tutte-Loop Equations

B. Eynard, 2016 .

All genus correlation functions for the hermitian 1-matrix model

B. Eynard, 2004, hep-th/0407261.

Enumeration of maps with self-avoiding loops and the model on random lattices of all topologies

B. Eynard, G. Borot, 2009, 0910.5896.

2-Matrix versus Complex Matrix Model, Integrals over the Unitary Group as Triangular Integrals

B. Eynard, A. Prats Ferrer, 2006 .

Mixed correlation functions in the 2-matrix model, and the Bethe Ansatz

B. Eynard, N. Orantin, 2005, hep-th/0504029.

2-Matrix versus Complex Matrix Model, Integrals over the Unitary Group as Triangular Integrals

B. Eynard, A. P. Ferrer, 2005, hep-th/0502041.

An analysis of the intermediate field theory of T4 tensor model

B. Eynard, S. Dartois, V. Nguyen, 2014, 1409.5751.

Supermatrix models, loop equations, and duality

B. Eynard, P. Desrosiers, 2009, 0911.1762.

Topological expansion of the chain of matrices

B. Eynard, A. P. Ferrer, 2008, 0805.1368.

Topological expansion and boundary conditions

B. Eynard, N. Orantin, 2007, 0710.0223.

A short note about Morozov's formula

B. Eynard, 2004, math-ph/0406063.

Resurgent Asymptotics of Jackiw–Teitelboim Gravity and the Nonperturbative Topological Recursion

B. Eynard, P. Gregori, Elba Garcia-Failde, 2023, Annales Henri Poincaré.

SPhT-T 14 / 033 , CRM-3335 A short overview of the ” Topological recursion ”

B. Eynard, 2019 .

Hamiltonian cycles on a random three-coordinate lattice

B. Eynard, E. Guitter, C. Kristjansen, 1998, cond-mat/9801281.

Coloring random triangulations

P. Francesco, B. Eynard, E. Guitter, 1997, cond-mat/9711050.

The asymptotic expansion of Tracy-Widom GUE law and symplectic invariants

B. Eynard, G. Borot, 2010, 1012.2752.

Tracy-Widom GUE law and symplectic invariants

B. Eynard, G. Borot, 2010, 1011.1418.

Mixed Correlation Functions of the Two-Matrix Model

B. Eynard, M. Bertola, 2003, hep-th/0303161.

Duality , Biorthogonal Polynomials and Multi – Matrix Models 1

B. Eynard, J. Harnad, M. Bertola, 2001 .

Topological recursion for generalised Kontsevich graphs and r-spin intersection numbers

B. Eynard, Elba Garcia-Failde, Séverin Charbonnier, 2021, 2105.08035.

Topological expansion of mixed correlations in the Hermitian 2-matrix model and x–y symmetry of the Fg algebraic invariants

B. Eynard, N. Orantin, 2008 .

From topological recursion to wave functions and PDEs quantizing hyperelliptic curves

B. Eynard, Elba Garcia-Failde, 2019, Forum of Mathematics, Sigma.

Geometrical interpretation of the topological recursion, and integrable string theories

B. Eynard, N. Orantin, 2009, 0911.5096.

Some properties of angular integrals

B. Eynard, M. Bergère, 2008, 0805.4482.

Local properties of the random Delaunay triangulation model and topological models of 2D gravity

Séverin Charbonnier, François David, Bertrand Eynard, 2017, Annales de l’Institut Henri Poincaré D.

Universal distribution of random matrix eigenvalues near the ‘birth of a cut’ transition

Bertrand Eynard, B. Eynard, 2006, math-ph/0605064.