Current Position
Chaire Professeur Junior, Laboratoire Analyse Géométrie Modélisation,This institute is part of CY Cergy Paris Université
P.I. of the European Research Council starting grant FloWAS (Flows, Waves, and their Asymptotic Stability).
Contact
charles.collot<youknowwhattoput>cyu.frUFR Sciences et Techniques,
AGM - Département Mathématiques,
Bâtiment E, cinquième étage
2 avenue Adolphe Chauvin,
95302, Cergy-Pontoise CEDEX
France.
Research interest
I work on qualitative properties of solutions of nonlinear evolution equations. This includes dynamics near solitons and self-similar solutions, in particular during singularity formation, or in asymptotic regimes such as long time dynamics, or regimes involving a statistical description. My research aims at understanding the behaviour of solutions to certain parabolic equations, wave equations, equations of fluid dynamics, and statistical physics problems.
Short curriculum vitae
Announcements
- (upcoming) 'Summer school: (in)-stability phenomena in fluid mechanics ' co-organized with Christophe Prange from May 27 to May 31, 2024 at CY Advanced Studies,
Mini-courses of 5 hours each by: Tarek Elgindi (Duke University), Philip Isett (California Institute of Technology), Sameer Iyer (University of California, Davis), Hao Jia (University of Minnesota)
Presentations of 1 hour by: Isabelle Gallagher (ENS Paris), Emmanuel Grenier (ENS Lyon) and Zineb Hassainia (NYUAD)
- (upcoming) 'Workshop Nonlinear Partial Differential Equations ' co-organized with Van Tien Nguyen from April 8 to 10, 2024 at NCTS Taipei
Confirmed speakers: Victor Aguilar (NTU), Hantaek Bae (Ulsan NIST), Siao Hao Guo (NTU), Kin Ming Hui (Academia Sinica), Soonsik Kwon (Korean AIST), Donghyun Lee (Postech),
Tai Ping Liu (Academia Sinica), Robert Marangell (U. Sydney), Hiroyoshi Mitake (U. Tokyo), Kenji Nakanishi (Kyoto U.), Takashi Suzuki (Osaka U.),
Zhian Wang (Hong-Kong Polytechnic U.), Chang Hong Wu (NYCU), Kung Chien Wu (NCKU), Yong Yu (Chinese U. Hong Kong)
Enseignement 2023-2024
- Semestre 1 : TP Modélisation, Master 2, voir la page web du cours.
- Semestre 2 : Singularités et temps long pour équations de fluide et de réaction-diffusion, Master 2. Notes de cours (not finalized, in French)
Preprints and Publications (preprints available on the arXiv)
- C. Collot, E. Danesi, A.-S. de Suzzoni and C. Maleze, Stability of homogeneous equilibria of the Hartree-Fock equation, for its equivalent formulation for random fields, 37 pages arXiv:2310.03442 , submitted
- C. Collot, P. Germain, Asymptotic stability of solitary waves for one dimensional nonlinear Schrödinger equations, 106 pages arXiv:2306.03668 , submitted
- C. Collot, T. Duyckaerts, C. Kenig and F. Merle, On classification of non-radiative solutions for various energy-critical wave equations, 72 pages arXiv:2211.16085 , to appear in Adv. Math.
- C. Collot, T. Duyckaerts, C. Kenig and F. Merle, On channels of energy for the radial linearised energy critical wave equation in the degenerate case, 36 pages arXiv:2211.16075 , Int. Math. Res. Not. 2022
- C. Collot, H. Dietert and P. Germain, Stability and cascades for the Kolmogorov-Zakharov spectrum of wave turbulence, 22 pages arXiv:2208.00947 , submitted
- C. Collot, T. Duyckaerts, C. Kenig and F. Merle, Soliton resolution for the radial quadratic wave equation in six space dimensions, 46 pages arXiv:2201.01848 , to appear in Vietnam J. Math.
- C. Collot, T.-E. Ghoul, N. Masmoudi and V. T. Nguyen, Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher, 33 pages arXiv:2112.15518 , J. Funct. Anal. 2023
- C. Collot, S. Ibrahim and Q. Lin, Stable Singularity Formation for the Inviscid Primitive Equations, 29 pages arXiv:2112.09759 , Ann. Inst. H. Poincaré Anal. Non Linéaire 2023
- I. Ampatzoglou, C. Collot, P. Germain, Derivation of the kinetic wave equation for quadratic dispersive problems in the inhomogeneous setting, 72 pages arXiv:2107.11819 , submitted
- C. Collot, P. Germain, Derivation of the homogeneous kinetic wave equation: longer time scales, 52 pages arXiv:2007.03508 , submitted
- C. Collot, A.-S. de Suzzoni, Stability of Steady States for Hartree and Schrodinger Equations for Infinitely Many Particles, 46 pages arXiv:2007.00472 , Ann. H. Lebesgue 2022
- C. Collot, P. Germain, On the derivation of the homogeneous kinetic wave equation, 42 pages arXiv:1912.10368 , to appear in Comm. Pure Appl. Math.
- C. Collot, T.-E. Ghoul, N. Masmoudi, V. T. Nguyen Spectral analysis for singularity formation of the two dimensional Keller-Segel system, 67 pages arXiv:1911.10884 , Ann. PDE 2022
- C. Collot, T.-E. Ghoul, N. Masmoudi, V. T. Nguyen Refined description and stability for singular solutions of the 2D Keller-Segel system, 48 pages arXiv:1912.00721 , Comm. Pure Appl. Math. 2022
- C. Collot, T.-E. Ghoul, N. Masmoudi, Singularities and unsteady separation for the inviscid two-dimensional Prandtl system, 64 pages arXiv:1903.08244 , Arch. Ration. Mech. Anal. 2021
- C. Collot, A.-S. de Suzzoni, Stability of equilibria for a Hartree equation for random fields, 24 pages arXiv:1811.03150 , J. Math. Pures App. 2020
- C. Collot, T.-E. Ghoul, S. Ibrahim, N. Masmoudi, On singularity formation for the two dimensional unsteady Prandtl's system around the axis, 79 pages arXiv:1808.05967 , J. Eur. Math. Soc. 2022
- C. Collot, T.-E. Ghoul, N. Masmoudi, Singularity formation for Burgers equation with transversal viscosity, 79 pages arXiv:1803.07826 , Ann. Sci. Ec. Norm. Supér. 2022.
- C. Collot, F. Merle, P. Raphaël, Strongly anisotropic type II blow-up at an isolated point, 66 pages arXiv:1709.04941, J. Amer. Math. Soc. 2020
- C. Collot, P. Raphaël, J. Szeftel, On the stability of type I blow up for the energy supercritical heat equation, 82 pages arXiv:1605.07337, Mem. Amer. Math. Soc. 2019
- C. Collot, F. Merle, P. Raphaël, Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions, major part of arXiv:1604.08323, Comm. Math. Phys. 2017
- C. Collot, F. Merle, P. Raphaël, Stability of ODE blow-up for the energy critical semilinear heat equation, minor part of arXiv:1604.08323, C. R. Math. Acad. Sci. Paris. 2017
- C. Collot, Non radial type II blow up for the energy supercritical semilinear heat equation, 105 pages arXiv:1604.02856, Anal. PDE 2017
- C. Collot, Type II blow up manifolds for a supercritical semi-linear wave equation, 142 pages arXiv:1407.4525, Mem. Amer. Math. Soc. 2018
Other documents
- Short lecture notes from a minicourse I gave at Chinese Academy of Sciences in 2023, aimed at graduate students. They introduce to singularity formation for the examples of the Burgers, inviscid homogeneous Prandtl, and Keller-Segel equations.
- Short lecture notes from a minicourse I gave at USTC in 2019. These are aimed at graduate students, presenting key features in singularity formation, some important techniques, via the examples of the semilinear heat equation and the Prandtl's system.
- The companion paper of the talk I gave on July 3, 2018, for the Laurent Schwartz seminar, entitled On self-similarity in singularities of the unsteady Prandtl's system and related problems.
- The companion paper of the talk A.-S. de Suzzoni gave for the Laurent Schwartz seminar, entitled Un resultat de diffusion pour l’equation de Hartree autour de solutions non localisees.
- The companion paper of the talk I gave at IHES on May 3, 2016, entitled On blow-up and dynamics near ground states for some semilinear equations.
- My PhD thesis that I defended in November 2016. Most of it is written in English, it contains an introduction to my research field, un résumé en français, and some long sketches of certain proofs appearing in my publications.