This institute is part of Cergy Paris Université.

UFR Sciences et Techniques,

AGM - Département Mathématiques,

Bâtiment E, cinquième étage

2 avenue Adolphe Chauvin,

95302, Cergy-Pontoise CEDEX

France.

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.

*Semestre 1 : Groupe de travail M1, groupe 1. Voir le descriptif du cours*

*I. Ampatzoglou, C. Collot, P. Germain, Derivation of the kinetic wave equation for quadratic dispersive problems in the inhomogeneous setting,**arXiv:2007.03508**C. Collot, P. Germain, Derivation of the homogeneous kinetic wave equation: longer time scales,**arXiv:2007.03508 , submitted**C. Collot, A.-S. de Suzzoni, Stability of Steady States for Hartree and Schrodinger Equations for Infinitely Many Particles,**arXiv:2007.00472 , submitted**C. Collot, P. Germain, On the derivation of the homogeneous kinetic wave equation,**arXiv:1912.10368 , submitted**C. Collot, T.-E. Ghoul, N. Masmoudi, V. T. Nguyen Refined description and stability for singular solutions of the 2D Keller-Segel system,**arXiv:1912.00721 , Comm. Pure Appl. Math., 2021**C. Collot, T.-E. Ghoul, N. Masmoudi, V. T. Nguyen Spectral analysis for singularity formation of the two dimensional Keller-Segel system,**arXiv:1911.10884 , submitted**C. Collot, T.-E. Ghoul, N. Masmoudi, Singularities and unsteady separation for the inviscid two-dimensional Prandtl system,**arXiv:1903.08244 , Arch. Ration. Mech. Anal., 2021**C. Collot, A.-S. de Suzzoni, Stability of equilibria for a Hartree equation for random fields,**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,**arXiv:1808.05967 , submitted**C. Collot, T.-E. Ghoul, N. Masmoudi, Singularity formation for Burgers equation with transversal viscosity,**arXiv:1803.07826 , to appear in Ann. Sci. Ec. Norm. Supér. .*- C. Collot, F. Merle, P. Raphaël,
*Strongly anisotropic type II blow-up at an isolated point,*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,*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,*arXiv:1604.02856, Anal. PDE., (2017) - C. Collot,
*Type II blow up manifolds for a supercritical semi-linear wave equation,*arXiv:1407.4525, Mem. Amer. Math. Soc., (2018)

- 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.