Alain Blaustein

Presentation

Welcome to my webpage. I am interested in the theoretical and numerical analysis of mean-field models arising in Biology and Physics.

I am a research scientist (chargé de recherche) in the Inria team RAPSODI in Lille.

I held a S. Chowla research assistant position at the Department of Mathematics of the Pennsylvania State University from August 2023 to December 2024.

My Ph.D. was defended in June 2023 and supervised by Pr. Francis Filbet at the Institut de Mathématiques de Toulouse.

This webpage gathers information and documents about my research, my teaching activities and my education.

Research

Pre-print:

• Longtime and chaotic dynamics in microscopic systems with singular interactions, (2024), with A. Béjar-López, P.-E. Jabin, J. Soler.
• Structure preserving solver for Multi-dimensional Vlasov-Poisson type equations, (2024).
• Derivation of the bacterial run-and-tumble kinetic model : quantitative and strong convergence results, (2023).

Publications:

• Concentration profiles in FitzHugh-Nagumo neural networks: A Hopf-Cole approach, Discrete Contin. Dyn. Syst. - B 29 (2024), no. 4, p. 2018-2042, with E. Bouin.
• A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model, J. Comput. Phys. 498 (2024), no. 112693, with F. Filbet.
• On a discrete framework of hypocoercivity for kinetic equations, AMS Math. Comp. 93 (2024), no. 345, p. 163-202, with F. Filbet.
• Diffusive limit of the Vlasov-Poisson-Fokker-Planck model: quantitative and strong convergence results, SIAM J. Math. Anal. 55 (2023), no. 5, p. 5464-5482.
• Large coupling in a FitzHugh-Nagumo neural network: quantitative and strong convergence results, J. Differential Equations 374 (2023), p. 218-266.
• Concentration phenomena in FitzHugh-Nagumo's equations: a mesoscopic approach, SIAM J. Math. Anal. 55 (2023), no. 1, p. 367-404, with F. Filbet.

Ph.D. thesis:

• Numerical and theoretical analysis of models arising in physics and biology (Étude numérique et analytique de modèles issus des neurosciences et de la physique), defended in June 2023: [pdf].

Conferences and Seminars

• EWM-EMS Summer School: Kinetic Theory Arising from Mathematical Biology, Institut Mittag-Leffler (Djursholm), 5th July 2024.
• PDE and numerical analysis seminar, Laboratoire J.A. Dieudonné (Nice), 30th May 2024.
• Journées Jeunes EDPistes en France, Institut de Mathématiques de Toulouse (Toulouse), 20th March 2024.
• Workshop on stability analysis for nonlinear PDEs, Pennsylvania State University (State College), 17th October 2023 : presentation.
• Webinar of the French-Korean IRL in Mathematics, 9th June 2023 : presentation.
• PDE seminar, IRMAR (Rennes), 23rd March 2023 : presentation.
• SIAM Conference on Computational Science and Engineering, RAI Congress Centre (Amsterdam), 26th February - 3rd March 2023 : presentation.
• Seminario de Ecuaciones Diferenciales, Departamento de Matemática Aplicada de la Universidad de Granada (Granada), 15th February 2023 : presentation.
• RSME 2023 LEON, Universidad de Leon (Leon), 6th - 10th February 2023 : presentation.
• Kinetic and hyperbolic equations: modeling, analysis and numerics, IMT (Toulouse), 12th - 16th December 2022 : presentation.
• International Conference on Mathematical Neuroscience , happening virtually, 7th July 2022 : presentation.
• Colloque ANR ChaMaNe, Ile Rousse, Corse, 22nd June 2022 : presentation.
• Frontiers in kinetic theory: connecting microscopic to macroscopic scales, Isaac Newton Institute (Cambridge), 17th May 2022 : presentation.
• SIAM Conference on Analysis of Partial Differential Equations, happening virtually, 14th - 18th March 2022 : presentation.
• Asymptotic Behaviors of systems of PDEs arising in physics and biology - 4th edition, Polytech Lille (Lille), 16th - 19th November 2021 : presentation.
• Modèles et méthodes pour les équations cinétiques, IMB (Bordeaux), 20th - 22nd October 2021 : presentation.
• Kinetic Coffee (organized by Pr. Clément Mouhot), happening virtually, 16th June 2021 : presentation.

Teaching

• 2023-2024 : Pennsylvania State University.
  • 4 unit course (49*1.5 ~ 73h eq. TD), calculus and analytic geometry II.
  • 4 unit course (49*1.5 ~ 73h eq. TD), calculus and analytic geometry II.
• 2022-2023 : Université Paul Sabatier.
  • 4h of pratictal works (Python), linear algebra, first year of BSc.
  • 30h of lecture and tutorials, linear algebra, first year of BSc.
• 2021-2022 : Université Paul Sabatier.
  • 26h of lecture and tutorials, linear algebra, first year of BSc.
  • 9h of pratictal works (Python), linear algebra, first year of BSc.
  • 30h of tutorials, mathematics, first year of BSc.
• 2020-2021 : Université Paul Sabatier.
  • 26h of lecture and tutorials, linear algebra, first year of BSc.
  • 30h of tutorials, mathematics, first year of BSc.

Resume

Contact me

alain.blaustein[at]inria[dot]fr