Biography
Isabelle Catto est docteure de l’Université Paris-Dauphine-PSL (1991) et chargée de recherches hors-classe au CNRS. Ses recherches portent sur l’étude de problèmes variationnels et d’équations aux dérivées partielles non linéaires issus de la mécanique quantique.
Elle est actuellement responsable pédagogique de la double licence Intelligence artificielle et sciences des organisations de l’Université Paris-Dauphine-PSL.
De 2014 à 2021, elle a été mise à disposition auprès de l’université PSL pour exercer des fonctions de vice-présidente en charge de la formation. Dans ce cadre, elle a mise en place te piloté deux nouvelles formations : le CPES en partenariat avec le Lycée Henri-IV et la licence Sciences pour un mode durable.
Publications
Articles
Catto I., Meng L., Paturel E., Séré É. (2024), Existence of minimizers for the Dirac-Fock Model of Crystals, Archive for Rational Mechanics and Analysis, vol. 248, n°63 
Catto I., Dolbeault J., Sánchez Ó., Soler J. (2013), Existence of steady states for the Maxwell-Schrödinger-Poisson system: exploring the applicability of the concentration-compactness principle, Mathematical Models and Methods in Applied Sciences, vol. 23, n°10, p. 1915-1938
Bardos C., Catto I., Mauser N., Trabelsi S. (2010), Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Archive for Rational Mechanics and Analysis, vol. 198, n°1, p. 273-330
Catto I., Bardos C., Mauser N., Trabelsi S. (2009), Global-in-time existence of solutions to the multiconfiguration time-dependent Hartree-Fock equations: A sufficient condition, Applied Mathematics Letters, vol. 22, n°2, p. 147-152
Valero J., Gimenez A., Amigo M., Catto I. (2009), Attractors for a non-linear parabolic equation modelling suspension flows, Discrete and Continuous Dynamical Systems. Series B, vol. 11, n°2, p. 205-231
Catto I., Cancès E., Gati Y. (2005), Mathematical analysis of a nonlinear parabolic equation arising in the modelling of non-newtonian flows, SIAM Journal on Mathematical Analysis, vol. 37, n°1, p. 60-82
Gati Y., Cancès E., Le Bris C., Catto I. (2005), Well-posedness of a multiscale model for concentrated suspensions, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, vol. 4, n°4, p. 1041-1058
Catto I., Hainzl C. (2004), Self-energy of one electron in non-relativistic QED, Journal of Functional Analysis, vol. 207, n°1, p. 68-110
Catto I., Exner P., Hainzl C. (2004), Enhanced binding revisited for a spinless particle in non-relativistic QED, Journal of Mathematical Physics, vol. 45, n°11, p. 4174-4185
Benguria R., Monneau R., Catto I., Dolbeault J. (2004), Oscillating minimizers of a fourth order problem invariant under scaling, Journal of Differential Equations, vol. 205, n°1, p. 253-269
Catto I., Lions P-L., Le Bris C. (2002), On some periodic Hartree-type models for crystals, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 19, n°2, p. 143-190
Le Bris C., Catto I., Lions P-L. (2001), On the thermodynamic limit for Hartree–Fock type models, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, vol. 18, n°6, p. 687-760
Catto I., Lions P-L., Le Bris C. (1998), Sur la limite thermodynamique pour des modèles de type Hartree et Hartree-Fock, Comptes rendus. Mathématique, vol. 327, n°3, p. 259-266
Catto I., Le Bris C., Lions P-L. (1996), Limite thermodynamique pour des modèles de type Thomas-Fermi, Comptes rendus. Mathématique, vol. 322, p. 357-364
Catto I., Lions P-L. (1993), Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 4 : Binding of neutral systems for the Hartree model, Communications in Partial Differential Equations, vol. 18, n°7-8, p. 1149-1159
Catto I. (1993), On some vector-valued non linear variational problems: variations on the Skyrme-Hartree-Fock model in nuclear physics, Differential and Integral Equations, vol. 6, n°2, p. 291-318
Catto I., Lions P-L. (1993), Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 2 : Stability is equivalent to the binding of neutral subsystems, Communications in Partial Differential Equations, vol. 18, n°1-2, p. 305-354
Catto I., Lions P-L. (1993), Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 3 : Binding of neutral subsystems, Communications in Partial Differential Equations, vol. 18, n°3-4, p. 381-429
Catto I., Lions P-L. (1992), A necessary and sufficient condition for the stability of general molecular systems, Communications in Partial Differential Equations, vol. 17, n°7-8, p. 1051-1110
Catto I., Lions P-L. (1990), La stabilité des molécules et la liaison des atomes pour des modèles de type Thomas-Fermi ou Hartree, Comptes rendus. Mathématique, vol. 311, p. 193-198
Ouvrages
Pons G., Catto I., Gentil I. (2011), Mathématiques L sciences éco : éléments de calcul différentiel pour l'économie : + exercices et problèmes corrigés, Paris: Ellipses , 288 p.
Catto I., Le Bris C., Lions P-L. (1998), Mathematical theory of thermodynamic limits. Thomas- Fermi type models, Oxford: Clarendon Press, 292 p.
Chapitres d'ouvrage
Catto I. (2015), Mathematical modelling of quantum crystals, in Björn Engquist, Encyclopedia of Applied and Computational Mathematics, Berlin Heidelberg: Springer
Catto I. (2015), Hartree-Fock type models, in Björn Engquist, Encyclopedia of Applied and Computational Mathematics, Berlin Heidelberg: Springer
Catto I., Lions P-L., Le Bris C. (2000), Recent mathematical results on the quantum modeling of crystals, in Mireille Defranceschi, Claude Le Bris, Mathematical models and methods for ab initio quantum chemistry, Edimbourg: Springer, p. 95-120
Prépublications / Cahiers de recherche
Catto I., Meng L. (2023), Properties of periodic Dirac--Fock functional and minimizers, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 32 p.