Curriculum Vitae Theéophile Dolmaire
Office 745,
Sophie Germain building, 8, place Aureélie Nemours, 75013, Paris,
France
E-mail : theophile.dolmaire@imj-prg.fr
Education
2010-2012 Student in Classes Preéparatoires (CPGE), PTSI then PT* Metz, then Paris, France (Competitive classes preparing to engineering schools such as Polytechnique or ENS) 2012-2016 Student in Eécole Normale Supeérieure de Cachan, Mathematics department
2016- PhD student, laboratory IMJ-PRG, Universiteé Paris Diderot (Paris 7)
Rigorous derivation of the Boltzmann equation and Lanford’s theorem for particles evolving in a domain with boundary conditions.
Advisors : Laurent Desvillettes (IMJ-PRG) and Isabelle Gallagher (IMJ-PRG, ENS Ulm)
Degrees
June 2013 Licence « Matheématiques Fondamentales », Universiteé Paris Diderot (Paris 7)
(Bachelor) mention Treès Bien (16,84/20)
July 2015 Concours of the « Agreégation externe de Matheématiques »
(French degree preparing for teaching in highschool of higher education)
July 2016 Master’s degree « Matheématiques Fondamentales », Universiteé Paris Diderot
(Paris 7) mention Treès Bien (16,6/20)
Research internship
March-May 2013 About Semigroups
Advisor : Samy Abbes. First steps in algebra and research, in the laboratory PPS, Universiteé Paris Diderot.
June 2013 About weak solutions of PDEs
Advisor : Freédeéric Pascal. First steps in PDEs analysis (Poisson equation) and numerical simulations (finite element method and dual mesh), in the laboratory CMLA, ENS Cachan.
May-July 2014 Algebra and probability
Advisor : Samy Abbes. Work in the laboratory PPS, Universiteé Paris Diderot, on trace monoids and probability laws on cones. Personal contribution : no such law can exist if the monoid is non trivial.
April-July 2016 Theorem of Lanford
Advisor : Laurent Desvillettes and Isabelle Gallagher.
Talks
May 2017 Group of students in PDEs, ENS Ulm : « Theéoreème de Lanford pour l’eéquation de Boltzmann »
December 2017 Group of students in PDEs, Jussieu : « Eéquation de Boltzmann : convergence vers l’eéquilibre et conjecture de Cercignani »
February 2018 PhD students seminary of the laboratory IMJ-PRG : « Eéquation de Boltzmann et convergence vers l’eéquilibre thermodynamique »
April 2018 PhD students seminary of the laboratory CEREMADE (Paris Dauphine) :
« Eéquation de Boltzmann et convergence vers l’eéquilibre thermodynamique »
Conferences and workshops
June 2016 Recent advances in kinetic equations and applications, Universiteé Pierre et Marie Curie (Paris 6), Paris
April 2017 PDE/Probability Interactions : Kinetic equations, Long time and Propagation of Chaos, CIRM, Marseille
May-June 2017 Advanced School & Workshop on Nonlocal Partial Differential Equations and Applications to Geometry, Physics and Probability, ICTP, Trieste June 2017 Journeées EDP, Roscoff (France)
July 2017 Fluids, dispersions and blow-up, Institut Henri Poincareé, Paris
October 2017 VIe Colloque EDP-Normandie, Universiteé de Caen-Normandie, Caen (France)
November 2017 Recent advances in kinetic equations and applications, Institut Henri Poincareé and Paris Dauphine, Paris
December 2017 Classical and Quantum Mechanical Models of Many-Particles Systems, Oberwolfach
March 2018 Mathematical Aspects of Fluids : kinetics and dynamics, ENS Ulm, Paris Workshop on kinetic and fluid Partial Differential Equations, Universiteé
Paris Descartes and Universiteé Paris Diderot
June 2019 Qualitative behaviour of kinetic equations and related problems : numerical and theoretical aspects, HIM, Bonn (Germany)
Research statement
My research work mixes the study of Partial Differential Equations and mathematical Physics, especially statistical mechanics, and is mainly focused on the rigorous derivation of the Boltzmann equation.
In 1973, Lanford published his pioneering work, in which he established a rigorous link between a particular description of a dilute gas and the Boltzmann equation, holding at a mesoscopic scale. He used two hierarchies, that is two sequences of equations, the first describing the dynamics of a finite number of particles, and the second being, up to considering factorized solutions, equivalent to the Boltzmann equation. On the one hand, he proved a result of existence of solutions for those two hierarchies simultaneously. On the other hand, he was able to show the convergence of the solutions of the BBGKY hierarchy towards the solutions of the Boltzmann one, in the Boltzmann-Grad limit. This theorem provided therefore a rigorous result describing the apparition of irreversibility from a reversible dynamics at a microscopic scale.
Following the improvements of the proof of the theorem due to Cercignani, Illner, Pulvirenti on the one hand, Gallagher, Saint-Raymond and Texier on the other hand, during the thesis I studied the case of particles moving around an obstacle lying in the Euclidian space. The domain of the system of particles is then the complement of a convex subset of the Euclidian space. The particles are interacting with each other as hard spheres, while the rebounds against the obstacle are assumed to be ruled by the law of specular reflection.
A challenging problem for the future consists in modifying the laws which govern the evolution of the particles. Firstly, a natural extension of the result stated by Lanford would consist in modifying the interaction between the particles and the obstacle. A difficult question, which would imply a radical change in the core of the proof and in the objects studied along it which define the hierarchies, would be to consider instead a diffusive boundary condition, or even a mixed condition, as in the article of Briant and Guo, which is more meaningful from the point of view of the applications.
Secondly, one can study the behaviour of the system when one enables a loss of kinetic energy during collisions (which are therefore inelastic). The Cauchy problem for the system of particles, when their number is fixed, which is the very first step of the proof of the Lanford’s theorem, is in itself a challenge.
Teaching
2015-2016 Oral examiner in Mathematics at Lyceée Janson de Sailly (Paris XVIe, for the MPSI4 class, undergraduate students preparing engineering schools and competitve exams)
First semester, 2016-2017 Elementary Analysis and Algebra for Biologists (Licence 1, 2h weekly)
Second semester, 2016-2017 Elementary Analysis and Algebra for Chemists (Licence 1, 3h weekly)
Second semester, 2017-2018 Advanced exercices and results for Licence 1 (2h weekly, for voluntary students)
Second semester 2017-2018 Ordinary Differential Equations (Licence 3, 3h weekly)
Second semester, 2018-2019 Advanced exercices and results for Licence 1 (2h weekly, for voluntary students)
Second semester 2018-2019 Ordinary Differential Equations (Licence 3, 3h weekly)
Administrative duties
2016- Representative of the PhD students at the council of the laboratory IMJ-PRG 2017-2018 Organiser of the meeting between Master and PhD students of the
laboratory IMJ-PRG
Miscellaneous
Linguistic skills French (native langage), English (fluent), German (basic)
