@article {MR3871555, title = {Discriminant circle bundles over local models of Strebel graphs and Boutroux curves}, journal = {Teoret. Mat. Fiz.}, volume = {197}, number = {2}, year = {2018}, pages = {163{\textendash}207}, issn = {0564-6162}, doi = {10.4213/tmf9513}, url = {https://doi.org/10.4213/tmf9513}, author = {Marco Bertola and Korotkin, D. A.} } @article {BeCaRu, title = {Noncommutative Painlev{\'e} Equations and Systems of Calogero Type}, journal = {Comm. Math. Phys}, year = {2018}, author = {Marco Bertola and Mattia Cafasso and V. Rubtsov} } @article {bertola2018painleve, title = {Painlev{\'e} IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane}, journal = {Symmetry, Integrability and Geometry. Methods and Applications}, volume = {14}, year = {2018}, publisher = {National Academy of Sciences of Ukraine}, abstract = {
We study the asymptotic behaviour of orthogonal polynomials in the complex plane that are associated to a certain normal matrix model. The model depends on a parameter and the asymptotic distribution of the eigenvalues undergoes a transition for a special value of the parameter, where it develops a corner-type singularity. In the double scaling limit near the transition we determine the asymptotic behaviour of the orthogonal polynomials in terms of a solution of the Painlev{\textasciiacute}e IV equation. We determine the Fredholm determinant associated to such solution and we compute it numerically on the real line, showing also that the corresponding Painlev{\textasciiacute}e transcendent is pole-free on a semiaxis.
}, doi = {10.3842/SIGMA.2018.091}, author = {Marco Bertola and Jos{\'e} Gustavo Elias Rebelo and Tamara Grava} } @article {Bertola:2016nr, title = {The Kontsevich matrix integral: convergence to the Painlev{\'e} hierarchy and Stokes{\textquoteright} phenomenon}, journal = {Comm. Math. Phys}, volume = {DOI 10.1007/s00220-017-2856-3}, year = {2017}, url = {http://arxiv.org/abs/1603.06420}, author = {Marco Bertola and Mattia Cafasso} } @article {MR3665212, title = {The Malgrange form and Fredholm determinants}, journal = {SIGMA Symmetry Integrability Geom. Methods Appl.}, volume = {13}, year = {2017}, pages = {Paper No. 046, 12}, issn = {1815-0659}, doi = {10.3842/SIGMA.2017.046}, url = {http://dx.doi.org/10.3842/SIGMA.2017.046}, author = {Marco Bertola} } @article {MR3663616, title = {Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schr{\"o}dinger Equation}, journal = {Comm. Math. Phys.}, volume = {354}, number = {2}, year = {2017}, pages = {525{\textendash}547}, issn = {0010-3616}, doi = {10.1007/s00220-017-2895-9}, url = {http://dx.doi.org/10.1007/s00220-017-2895-9}, author = {Marco Bertola and Alexander Tovbis} } @article {Bertola:2015tg, title = {Symplectic geometry of the moduli space of projective structures in homological coordinates}, journal = {Inventiones Mathematicae}, year = {2017}, month = {06}, pages = {1{\textendash}56}, url = {https://arxiv.org/abs/1506.07918}, author = {Marco Bertola and Dmitry Korotkin and Chaya Norton} } @article {MR3686488, title = {Universality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles}, journal = {Random Matrices Theory Appl.}, volume = {6}, number = {3}, year = {2017}, pages = {1750010, 22}, issn = {2010-3263}, doi = {10.1142/S2010326317500101}, url = {http://dx.doi.org/10.1142/S2010326317500101}, author = {Marco Bertola and Mattia Cafasso} } @article {PhysRevLett.119.033901, title = {Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schr{\"o}dinger Equation}, journal = {Phys. Rev. Lett.}, volume = {119}, year = {2017}, month = {Jul}, pages = {033901}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.119.033901}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.033901}, author = {Tikan, Alexey and Billet, Cyril and Gennady El and Alexander Tovbis and Marco Bertola and Sylvestre, Thibaut and Gustave, Francois and Randoux, Stephane and Genty, Go{\"e}ry and Suret, Pierre and Dudley, John M.} } @article {MR3589917, title = {On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight}, journal = {SIGMA Symmetry Integrability Geom. Methods Appl.}, volume = {12}, year = {2016}, pages = {Paper No. 118, 50 pages}, issn = {1815-0659}, doi = {10.3842/SIGMA.2016.118}, url = {http://dx.doi.org/10.3842/SIGMA.2016.118}, author = {Marco Bertola and Alexander Tovbis} } @article {MR3505204, title = {Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$}, journal = {Phys. D}, volume = {327}, year = {2016}, pages = {30{\textendash}57}, issn = {0167-2789}, doi = {10.1016/j.physd.2016.04.008}, url = {http://dx.doi.org/10.1016/j.physd.2016.04.008}, author = {Marco Bertola and Boris Dubrovin and Di Yang} } @article {BertolaCorrection, title = {CORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function}, year = {2016}, month = {01}, url = {http://arxiv.org/abs/1601.04790}, author = {Marco Bertola} } @article {BertoBothBalogh, title = {Hankel determinant approach to generalized Vorob{\textquoteright}ev-Yablonski polynomials and their roots}, journal = {Constr. Approx.}, volume = {44}, number = {3}, year = {2016}, pages = {417{\textendash}453}, issn = {0176-4276}, doi = {10.1007/s00365-016-9328-4}, url = {http://dx.doi.org/10.1007/s00365-016-9328-4}, author = {Ferenc Balogh and Marco Bertola and Thomas Bothner} } @article {MR3592329, title = {Rogue waves in multiphase solutions of the focusing nonlinear Schr{\"o}dinger equation}, journal = {Proc. A.}, volume = {472}, number = {2194}, year = {2016}, pages = {20160340, 12}, issn = {1364-5021}, doi = {10.1098/rspa.2016.0340}, url = {http://dx.doi.org/10.1098/rspa.2016.0340}, author = {Marco Bertola and Gennady El and Alexander Tovbis} } @article {BertoDiDub, title = {Simple Lie Algebras and Topological ODEs}, journal = {Int. Math. Res. Not.}, volume = {2016}, number = {rnw285}, year = {2016}, author = {Marco Bertola and Boris Dubrovin and Di Yang} } @article {BKT-sobolev, title = {On Sobolev instability of the interior problem of tomography}, journal = {Journal of Mathematical Analysis and Applications}, year = {2016}, author = {Marco Bertola and Alexander Katsevich and Alexander Tovbis} } @article {MR3346719, title = {Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlev{\'e} equation}, journal = {Constr. Approx.}, volume = {41}, number = {3}, year = {2015}, pages = {529{\textendash}587}, issn = {0176-4276}, doi = {10.1007/s00365-015-9288-0}, url = {http://dx.doi.org/10.1007/s00365-015-9288-0}, author = {Marco Bertola and Alexander Tovbis} } @article {MR3369874, title = {A degeneration of two-phase solutions of the focusing nonlinear Schr{\"o}dinger equation via Riemann-Hilbert problems}, journal = {J. Math. Phys.}, volume = {56}, number = {6}, year = {2015}, pages = {061507, 17}, issn = {0022-2488}, doi = {10.1063/1.4922362}, url = {http://dx.doi.org/10.1063/1.4922362}, author = {Marco Bertola and Giavedoni, Pietro} } @article {MR3305428, title = {Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves}, journal = {Anal. Math. Phys.}, volume = {5}, number = {1}, year = {2015}, pages = {1{\textendash}22}, issn = {1664-2368}, doi = {10.1007/s13324-014-0088-7}, url = {http://dx.doi.org/10.1007/s13324-014-0088-7}, author = {Marco Bertola and Alexander Tovbis} } @article {MR3342766, title = {The partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy}, journal = {J. Phys. A}, volume = {48}, number = {19}, year = {2015}, pages = {195205, 20}, issn = {1751-8113}, doi = {10.1088/1751-8113/48/19/195205}, url = {http://dx.doi.org/10.1088/1751-8113/48/19/195205}, author = {Marco Bertola and Di Yang} } @article {MR3280250, title = {Strong asymptotics of the orthogonal polynomials with respect to a measure supported on the plane}, journal = {Comm. Pure Appl. Math.}, volume = {68}, number = {1}, year = {2015}, pages = {112{\textendash}172}, issn = {0010-3640}, doi = {10.1002/cpa.21541}, url = {http://dx.doi.org/10.1002/cpa.21541}, author = {Ferenc Balogh and Marco Bertola and Lee, Seung-Yeop and Kenneth McLaughlin} } @article {Bertola-Bothner-MeijerG, title = {Universality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices}, journal = {Commun. Math. Phys.}, volume = {337}, number = {3}, year = {2015}, month = {08}, pages = {1077{\textendash}1141}, doi = {10.1007/s00220-015-2327-7}, url = {http://link.springer.com/article/10.1007/s00220-015-2327-7}, author = {Marco Bertola and Thomas Bothner} } @article {MR3162486, title = {Cauchy-Laguerre two-matrix model and the Meijer-G random point field}, journal = {Comm. Math. Phys.}, volume = {326}, number = {1}, year = {2014}, pages = {111{\textendash}144}, issn = {0010-3616}, doi = {10.1007/s00220-013-1833-8}, url = {http://dx.doi.org/10.1007/s00220-013-1833-8}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {BertolaCafasso5, title = {Darboux Transformations and Random Point Processes}, journal = {IMRN}, volume = {rnu122}, year = {2014}, pages = {56}, author = {Marco Bertola and Mattia Cafasso} } @article {berto-Tovbis-Katsevich-CPAM, title = {Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach}, journal = {Comm. Pure Appl. Math.}, year = {2014}, author = {Marco Bertola and Alexander Katsevich and Alexander Tovbis} } @article {Berto-Bothner-YV, title = {Zeros of Large Degree Vorob{\textquoteright}ev-Yablonski Polynomials via a Hankel Determinant Identity}, journal = {International Mathematics Research Notices}, volume = {rnu239}, year = {2014}, author = {Marco Bertola and Thomas Bothner} } @article {BertolaCafasso4, title = {The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation}, journal = {Random Matrices: Theory and Applications}, volume = {02}, number = {02}, year = {2013}, pages = {1350003}, doi = {10.1142/S2010326313500032}, url = {http://www.worldscientific.com/doi/abs/10.1142/S2010326313500032}, author = {Marco Bertola and Mattia Cafasso} } @article {BertolaKatsevichTovbis1, title = {Inversion formulae for the $\romancosh$-weighted Hilbert transform}, journal = {Proc. Amer. Math. Soc.}, volume = {141}, number = {8}, year = {2013}, pages = {2703{\textendash}2718}, issn = {0002-9939}, doi = {10.1090/S0002-9939-2013-11642-4}, url = {http://dx.doi.org/10.1090/S0002-9939-2013-11642-4}, author = {Marco Bertola and Katsevich, A. and Alexander Tovbis} } @article {MR3117621, title = {Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes}, journal = {J. Stat. Phys.}, volume = {153}, number = {4}, year = {2013}, pages = {654{\textendash}697}, issn = {0022-4715}, doi = {10.1007/s10955-013-0845-2}, url = {http://dx.doi.org/10.1007/s10955-013-0845-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {MR3088819, title = {Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model}, journal = {J. Math. Phys.}, volume = {54}, number = {4}, year = {2013}, pages = {043517, 25}, issn = {0022-2488}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {BertolaTovbisNLS2, title = {Universality for the focusing nonlinear Schr{\"o}dinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronqu{\'e}e solution to Painlev{\'e} I}, journal = {Comm. Pure Appl. Math.}, volume = {66}, number = {5}, year = {2013}, pages = {678{\textendash}752}, issn = {0010-3640}, doi = {10.1002/cpa.21445}, url = {http://dx.doi.org/10.1002/cpa.21445}, author = {Marco Bertola and Alexander Tovbis} } @article {BertolaCafasso3, title = {Fredholm determinants and pole-free solutions to the noncommutative Painlev{\'e} II equation}, journal = {Comm. Math. Phys.}, volume = {309}, number = {3}, year = {2012}, pages = {793{\textendash}833}, issn = {0010-3616}, doi = {10.1007/s00220-011-1383-x}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x}, author = {Marco Bertola and Mattia Cafasso} } @article {Bertola:P2poles, title = {On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev{\'e} equation}, journal = {Nonlinearity}, volume = {25}, number = {4}, year = {2012}, pages = {1179{\textendash}1185}, issn = {0951-7715}, doi = {10.1088/0951-7715/25/4/1179}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/1179}, author = {Marco Bertola} } @article {BertolaCafasso2, title = {Riemann{\textendash}Hilbert approach to multi-time processes: The Airy and the Pearcey cases}, journal = {Physica D: Nonlinear Phenomena}, volume = {241}, number = {23-24}, year = {2012}, note = {Integrable Systems in Pure and Applied Mathematics}, pages = {2237 - 2245}, keywords = {Integrable kernels}, issn = {0167-2789}, doi = {10.1016/j.physd.2012.01.003}, url = {http://www.sciencedirect.com/science/article/pii/S0167278912000115}, author = {Marco Bertola and Mattia Cafasso} } @article {MR2880030, title = {Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes}, journal = {J. Stat. Phys.}, volume = {146}, number = {3}, year = {2012}, pages = {475{\textendash}518}, issn = {0022-4715}, doi = {10.1007/s10955-011-0409-2}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {Bertola:Boutroux, title = {Boutroux curves with external field: equilibrium measures without a variational problem}, journal = {Anal. Math. Phys.}, volume = {1}, number = {2-3}, year = {2011}, pages = {167{\textendash}211}, issn = {1664-2368}, doi = {10.1007/s13324-011-0012-3}, url = {http://dx.doi.org/10.1007/s13324-011-0012-3}, author = {Marco Bertola} } @article {BertolaCafasso1, title = {The Transition between the Gap Probabilities from the Pearcey to the Airy Process{\textendash}a Riemann-Hilbert Approach}, journal = {International Mathematics Research Notices}, volume = {doi: 10.1093/imrn/rnr066}, year = {2011}, pages = {1-50}, author = {Marco Bertola and Mattia Cafasso} } @article {Bertola:CBOPs, title = {Cauchy biorthogonal polynomials}, journal = {J. Approx. Theory}, volume = {162}, number = {4}, year = {2010}, pages = {832{\textendash}867}, issn = {0021-9045}, doi = {10.1016/j.jat.2009.09.008}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.008}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {BertolaIsoTau, title = {The dependence on the monodromy data of the isomonodromic tau function}, journal = {Comm. Math. Phys.}, volume = {294}, number = {2}, year = {2010}, pages = {539{\textendash}579}, issn = {0010-3616}, doi = {10.1007/s00220-009-0961-7}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-7}, author = {Marco Bertola} } @article {Bertola:wj, title = {First colonization of a hard-edge in random matrix theory}, journal = {Constr. Approx.}, volume = {31}, number = {2}, year = {2010}, pages = {231{\textendash}257}, issn = {0176-4276}, doi = {10.1007/s00365-009-9052-4}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-4}, author = {Marco Bertola and Lee, S. Y.} } @article {BertolaTovbis1, title = {Universality in the profile of the semiclassical limit solutions to the focusing nonlinear Schr{\"o}dinger equation at the first breaking curve}, journal = {Int. Math. Res. Not. IMRN}, number = {11}, year = {2010}, pages = {2119{\textendash}2167}, issn = {1073-7928}, doi = {10.1093/imrn/rnp196}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp196}, author = {Marco Bertola and Alexander Tovbis} } @article {Bertola:CauchyMM, title = {The Cauchy two{\textendash}matrix model}, journal = {Comm. Math. Phys.}, volume = {287}, number = {3}, year = {2009}, pages = {983{\textendash}1014}, author = {Marco Bertola and M Gekhtman and J Szmigielski} } @article {BertolaAdvances, title = {Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights}, journal = {Adv. Math.}, volume = {220}, number = {1}, year = {2009}, pages = {154{\textendash}218}, issn = {0001-8708}, author = {Marco Bertola and Mo, M. Y.} } @article {Bertola:Cubic, title = {Cubic string boundary value problems and Cauchy biorthogonal polynomials}, journal = {J. Phys. A}, volume = {42}, number = {45}, year = {2009}, pages = {454006, 13}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/45/454006}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/454006}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {Bertola:Lee, title = {First colonization of a spectral outpost in random matrix theory}, journal = {Constr. Approx.}, volume = {30}, number = {2}, year = {2009}, pages = {225{\textendash}263}, issn = {0176-4276}, doi = {10.1007/s00365-008-9026-y}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y}, author = {Marco Bertola and Lee, S. Y.} } @article {BertolaLeeMo, title = {Mesoscopic colonization in a spectral band}, journal = {J. Phys. A}, volume = {42}, number = {41}, year = {2009}, pages = {415204, 17}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/41/415204}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/415204}, author = {Marco Bertola and Lee, S. Y. and Mo, M. Y.} } @article {Bertola:MomentTau, title = {Moment determinants as isomonodromic tau functions}, journal = {Nonlinearity}, volume = {22}, number = {1}, year = {2009}, pages = {29{\textendash}50}, author = {Marco Bertola} } @article {Bertola:IZtau, title = {The partition function of the two-matrix model as an isomonodromic τ function}, journal = {J. Math. Phys.}, volume = {50}, number = {1}, year = {2009}, pages = {013529, 17}, issn = {0022-2488}, doi = {10.1063/1.3054865}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1063/1.3054865}, author = {Marco Bertola and Marchal, O.} } @article {BertolaBalogh, title = {Regularity of a vector potential problem and its spectral curve}, journal = {J. Approx. Theory}, volume = {161}, number = {1}, year = {2009}, pages = {353{\textendash}370}, issn = {0021-9045}, doi = {10.1016/j.jat.2008.10.010}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2008.10.010}, author = {Ferenc Balogh and Marco Bertola} } @article {MR2525872, title = {Topological expansion for the Cauchy two-matrix model}, journal = {J. Phys. A}, volume = {42}, number = {33}, year = {2009}, pages = {335201, 28}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/33/335201}, url = {http://dx.doi.org/10.1088/1751-8113/42/33/335201}, author = {Marco Bertola and Ferrer, A. Prats} } @article {MR2435752, title = {Harish-Chandra integrals as nilpotent integrals}, journal = {Int. Math. Res. Not. IMRN}, number = {16}, year = {2008}, pages = {Art. ID rnn062, 15}, issn = {1073-7928}, author = {Marco Bertola and Ferrer, Aleix Prats} } @article {Bertola:LOPs, title = {Biorthogonal Laurent polynomials, T{\"o}plitz determinants, minimal Toda orbits and isomonodromic tau functions}, journal = {Constr. Approx.}, volume = {26}, number = {3}, year = {2007}, pages = {383{\textendash}430}, issn = {0176-4276}, author = {Marco Bertola and Gekhtman, M.} } @article {Bertola:semiclassBOPsJAT, title = {Biorthogonal polynomials for two-matrix models with semiclassical potentials}, journal = {J. Approx. Theory}, volume = {144}, number = {2}, year = {2007}, pages = {162{\textendash}212}, issn = {0021-9045}, author = {Marco Bertola} } @article {Bertola:EffectiveIMRN, title = {Effective inverse spectral problem for rational Lax matrices and applications}, journal = {Int. Math. Res. Not. IMRN}, number = {23}, year = {2007}, pages = {Art. ID rnm103, 39}, issn = {1073-7928}, author = {Marco Bertola and Gekhtman, M.} } @inbook {Bertola:MasslessdeSitter, title = {Massless scalar field in a two-dimensional de Sitter universe}, booktitle = {Rigorous quantum field theory}, series = {Progr. Math.}, volume = {251}, year = {2007}, pages = {27{\textendash}38}, publisher = {Birkh{\"a}user}, organization = {Birkh{\"a}user}, address = {Basel}, author = {Marco Bertola and Corbetta, Francesco and Moschella, Ugo} } @article {Bertola:PDEBOPs, title = {The PDEs of biorthogonal polynomials arising in the two-matrix model}, journal = {Math. Phys. Anal. Geom.}, volume = {9}, number = {1}, year = {2006}, pages = {23{\textendash}52}, issn = {1385-0172}, author = {Marco Bertola and B. Eynard} } @article {Bertola:Semiiso, title = {Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions}, journal = {Comm. Math. Phys.}, volume = {263}, number = {2}, year = {2006}, pages = {401{\textendash}437}, issn = {0010-3616}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @article {Bertola:2MM_extendedWhitham, title = {Two-matrix model with semiclassical potentials and extended Whitham hierarchy}, journal = {J. Phys. A}, volume = {39}, number = {28}, year = {2006}, pages = {8823{\textendash}8855}, issn = {0305-4470}, author = {Marco Bertola} } @article {Bertola:Isomono_resonant, title = {Isomonodromic deformation of resonant rational connections}, journal = {IMRP Int. Math. Res. Pap.}, number = {11}, year = {2005}, pages = {565{\textendash}635}, issn = {1687-3017}, author = {Marco Bertola and Mo, M. Y.} } @article {Bertola:BilinearJAT, title = {Bilinear semiclassical moment functionals and their integral representation}, journal = {J. Approx. Theory}, volume = {121}, number = {1}, year = {2003}, pages = {71{\textendash}99}, issn = {0021-9045}, author = {Marco Bertola} } @article {Bertola:DifferentialCMP, title = {Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem}, journal = {Comm. Math. Phys.}, volume = {243}, number = {2}, year = {2003}, pages = {193{\textendash}240}, issn = {0010-3616}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @article {Bertola:Duality, title = {The duality of spectral curves that arises in two-matrix models}, journal = {Teoret. Mat. Fiz.}, volume = {134}, number = {1}, year = {2003}, pages = {32{\textendash}45}, issn = {0564-6162}, author = {Marco Bertola and B. Eynard and Kharnad, Dzh.} } @article {Bertola:FreeEnergyNPB, title = {Free energy of the two-matrix model/dToda tau-function}, journal = {Nuclear Phys. B}, volume = {669}, number = {3}, year = {2003}, pages = {435{\textendash}461}, issn = {0550-3213}, author = {Marco Bertola} } @article {Bertola:MixedJPA, title = {Mixed correlation functions of the two-matrix model}, journal = {J. Phys. A}, volume = {36}, number = {28}, year = {2003}, pages = {7733{\textendash}7750}, issn = {0305-4470}, author = {Marco Bertola and B. Eynard} } @article {Bertola:PartitionJPA, title = {Partition functions for matrix models and isomonodromic tau functions}, journal = {J. Phys. A}, volume = {36}, number = {12}, year = {2003}, note = {Random matrix theory}, pages = {3067{\textendash}3083}, issn = {0305-4470}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @article {Bertola:JPA, title = {Second and third order observables of the two-matrix model}, journal = {J. High Energy Phys.}, number = {11}, year = {2003}, pages = {062, 30 pp. (electronic)}, issn = {1126-6708}, author = {Marco Bertola} } @article {Bertola:CoherentJMP, title = {Coherent state realizations of $\rm su(n+1)$ on the $n$-torus}, journal = {J. Math. Phys.}, volume = {43}, number = {7}, year = {2002}, pages = {3425{\textendash}3444}, issn = {0022-2488}, author = {de Guise, Hubert and Marco Bertola} } @article {Bertola:DualityCMP, title = {Duality, biorthogonal polynomials and multi-matrix models}, journal = {Comm. Math. Phys.}, volume = {229}, number = {1}, year = {2002}, pages = {73{\textendash}120}, issn = {0010-3616}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @inbook {Bertola:JacobiCRM, title = {Jacobi groups, Jacobi forms and their applications}, booktitle = {Isomonodromic deformations and applications in physics (Montr{\'e}al, QC, 2000)}, series = {CRM Proc. Lecture Notes}, volume = {31}, year = {2002}, pages = {99{\textendash}111}, publisher = {Amer. Math. Soc.}, organization = {Amer. Math. Soc.}, address = {Providence, RI}, author = {Marco Bertola} } @article {Bertola:LietripleRMA, title = {Lie triple systems and warped products}, journal = {Rend. Mat. Appl. (7)}, volume = {21}, number = {1-4}, year = {2001}, pages = {275{\textendash}293}, issn = {1120-7183}, author = {Marco Bertola and Gouthier, D.} } @article {Bertola:Warped, title = {Warped products with special Riemannian curvature}, journal = {Bol. Soc. Brasil. Mat. (N.S.)}, volume = {32}, number = {1}, year = {2001}, pages = {45{\textendash}62}, issn = {0100-3569}, author = {Marco Bertola and Gouthier, Daniele} } @article {Bertola:DecomposingNPB, title = {Decomposing quantum fields on branes}, journal = {Nuclear Phys. B}, volume = {581}, number = {1-2}, year = {2000}, pages = {575{\textendash}603}, issn = {0550-3213}, author = {Marco Bertola and Bros, Jacques and Gorini, Vittorio and Moschella, Ugo and Schaeffer, Richard} } @article {Bertola:Frobenius1, title = {Frobenius manifold structure on orbit space of Jacobi groups. I}, journal = {Differential Geom. Appl.}, volume = {13}, number = {1}, year = {2000}, pages = {19{\textendash}41}, issn = {0926-2245}, author = {Marco Bertola} } @article {Bertola:Frobenius2, title = {Frobenius manifold structure on orbit space of Jacobi groups. II}, journal = {Differential Geom. Appl.}, volume = {13}, number = {3}, year = {2000}, pages = {213{\textendash}233}, issn = {0926-2245}, author = {Marco Bertola} } @article {Bertola:CFTNPB, title = {A general construction of conformal field theories from scalar anti-de Sitter quantum field theories}, journal = {Nuclear Phys. B}, volume = {587}, number = {1-3}, year = {2000}, pages = {619{\textendash}644}, issn = {0550-3213}, author = {Marco Bertola and Bros, Jacques and Moschella, Ugo and Schaeffer, Richard} } @article {Bertola:CorrespondencePLB, title = {Correspondence between Minkowski and de Sitter quantum field theory}, journal = {Phys. Lett. B}, volume = {462}, number = {3-4}, year = {1999}, pages = {249{\textendash}253}, issn = {0370-2693}, author = {Marco Bertola and Gorini, Vittorio and Moschella, Ugo and Schaeffer, Richard} } @article {Bertola:GenerationGC, title = {Generation of primordial fluctuations in curved spaces}, journal = {Gravit. Cosmol.}, volume = {4}, number = {2}, year = {1998}, pages = {121{\textendash}127}, issn = {0202-2893}, author = {Schaeffer, Richard and Moschella, Ugo and Marco Bertola and Gorini, Vittorio} }