I am an "Agrégé Préparateur" at ENS de Lyon and therefore a member of UMPA in the PDE and modelisation group. Before that, I was a PhD student at IRMAR, Université de Rennes 1, in the Research Group in Partial Differential Equations under the supervision of Prof. Karel Pravda-Starov. I was also a teaching assistant at ENS Rennes.
Here is a short cv in French.
Contact
UMPA - ENS de Lyon - Office MGN1.419.
Email: paul.alphonse at ens-lyon.fr.
Phone: +33 (0)4 72 72 81 88.
Research
Research interests
Smoothness, localization and integrability of solutions to linear evolution equations.
Stabilization and null-controllability of degenerate parabolic equations of hypoelliptic type.
Null-controllability of dispersive equations.
Subelliptic and hypoelliptic estimates for non-selfadjoint operators.
Preprints
A smoothing effect for the fractional Schrödinger equations on the circle and observability (avec N. Tzvetkov) [arXiv].
Unique continuation estimates for Baouendi-Grushin equations on cylinders (avec A. Seelmann) [arXiv].
Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability (with A. Seelmann) [arXiv].
Hypoelliptic estimates for linear transport operators [arXiv].
Peer-reviewed papers
Null-controllability of evolution equations associated with fractional Shubin operators through quantitative Agmon estimates [arXiv].
To appear in Annales de l'Institut Fourier.Null-controllability for weakly dissipative heat-like equations (with A. Koenig) [arXiv].
Evolution Equations and Control Theory 13 (2024), no. 3, pp. 973-988.Gains of integrability and local smoothing effects for quadratic evolution equations (with J. Bernier) [arXiv].
Journal of Functional Analysis 285 (2023), 110119, 35 pp.Approximate null-controllability with uniform cost for the hypoelliptic Ornstein-Uhlenbeck equations (with J. Martin) [arXiv].
SIAM Journal on Control and Optimization 61 (2023), pp. 1679-1711.Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects (with J. Bernier) [arXiv].
Annales scientifiques de l'École normale supérieure (4) 56 (2023), no. 2, pp. 323-382.Description of the smoothing effects of semigroups generated by fractional Ornstein-Uhlenbeck operators and subelliptic estimates [arXiv].
Journal of Evolution Equations 22 (2022), no. 28, 25 pp.Stabilization and approximate null-controllability for a large class of diffusive equations from thick control supports (with J. Martin) [arXiv].
ESAIM: Control, Optimization and Calculus of Variations 28 (2022), no. 16, 30 pp.Quadratic differential equations: partial Gelfand-Shilov smoothing effect and null-controllability [arXiv].
Journal of the Institute of Mathematics of Jussieu 20 (2021), no. 6, pp. 1749-1801.Smoothing properties of fractional Ornstein-Uhlenbeck semigroups and null-controllability (with J. Bernier) [arXiv].
Bulletin des Sciences Mathématiques 165 (2020), 102914, 52 pp.
Thesis
Régularité des solutions et contrôlabilité d'équations d'évolution associées à des opérateurs non autoadjoints, defended on 5 June 2020 [manuscript].