Alain Blaustein - Pennsylvania State University

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 S. Chowla Research Assistant at the Department of Mathematics of the Pennsylvania State University.

My Ph.D. was defended in June 2023 and supervised by 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

You can download a detailed CV here.

Education :

2020-2023 : Ph.D. in mathematics, Institut de mathématiques de Toulouse.
2016-2020 : ENS Rennes, Université de Rennes 1.

MSc in mathematics, with high honours.
Preparation year for the agrégation externe de mathématiques.
First year of a MSc in mathematics.
BSc in mathematics.

2014-2016 : Classe préparatoire MPSI - MP^*, Lycée Charlemagne, Paris.

Awards and scholarships :

2019 : Agrégation externe de mathématiques.

Internships :

2020 : Four months MSc internship at the Institut de mathématiques de Toulouse, France, with Prof. Francis Filbet. Mean Field limit for a FitzHug-Nagumo neural network with noise.
2019 : Two months internship at the Université Rennes 1, France, with Prof. Roger Lewandowski. Local well posedness of the incompressible Navier-Stokes equations.
2018 : Two months internship at the University of Chicago, US, with Prof. Guillaume Bal. Stochastic Homogenization.
2017 : Six weeks internship at Institut Fourier, France, with Prof. Pierre Dehornoy. Birkhoff sections of the geodesic flow in the torus.

Contact me

akb7016[at]psu[dot]edu