I am a postdoctoral researcher in mathematical quantum physics at Cermics, the laboratory of mathematics of the École des ponts, in the team of Éric Cancès. You can email me on long.meng@enpc.fr.
My main research interests are relativistic and non-relativistic mathematical quantum mechanics, functional analysis, harmonic analysis, Strichartz estimate, numerical analysis and spectral theory.
• Mar. 2022 - Now: postdoc at Cermics, École des ponts, in the team of Éric Cancès.
• Feb. 2021 - Jan. 2022: postdoc in Department of Mathematics, University of Padua, Italy, in the team of Federico Cacciafesta.
• 2017 - 2020 : PhD in mathematical physics at the University Paris-Dauphine, with Éric Séré
• 2016 - 2017 : Master's degree in mathematics, University Paris-Dauphine, Paris
• 2012 - 2016 : Bechelor's degree in Mathematics, University of Tongji, Shanghai
• 2020-2021: Numerical methods: matrix algebra and function of a real variable, L2, University Paris-Dauphine
[8] Properties of periodic Dirac--Fock functional and minimizers, with I. Catto, submitted.
[7] Strichartz estimates for the half wave/Klein-Gordon and Dirac Equations on compact manifolds without boundary, with F. Cacciafesta and E. Danesi, Math. Annalen, to appear.
[6] A rigorous justification of Mittleman's approach to the Dirac--Fock model, submitted.
[5] Existence of minimizers for the Dirac-Fock Model of Crystals, with I. Catto, E. Paturel and E. Séré, submitted.
[4] Strichartz estimates for the Dirac equation on asymptotically flat manifolds, with F. Cacciafesta and A.-S. de Suzzoni, Ann. Sc. Norm. Super. Pisa Cl. Sci, to appear.
[3] Large time well-posedness for a Dirac-Klein Gordon system, with F. Cacciafesta, A.-S. de Suzzoni and J. Sok, Nonlinear Anal. 239 (2024) 113420.
[2] Mixed regularity of N-body Schrödinger evolution equation and corresponding hyperbolic cross space approximation, submitted.
[1] On the mixed regularity of N-body Coulombic wavefunctions, ESAIM: M2AN 57 (2023) 2257–2282.
• The Mathematics and Physics of Moire Superlattices, Banff, Oct. 22-27, 2023
• EMC2 meeting, Roscoff, July 3-7, 2023
• Moire Materials Workshop, CCQ, May 30-June 02, 2023
• 15th meeting of the GDR DYNQUA, Rennes, Feb. 01-03, 2023
• The analysis of relativistic quantum systems Analyse de systèmes quantiques relativistes, Marseille, Jan. 09-13, 2023
• QM 2D Moiré Scale mini-workshop, IPAM, May 18-20, 2022
• PDEs and Relativistic Quantum Mechanics, University of Côte d'Azur, May 11-13, 2022
• The Analysis of Complex Quantum Systems: Large Coulomb Systems and Related Matters, CIRM, October 21-25 2019
• Nonlinear Dirac equations and related problems, Bielefeld University, May 28-30, 2018
• Arizona School of Analysis and Mathematical Physics, University of Arizona, March 5-9, 2018
• Ludwig Maximilian University of Munich, Apr.18-20, 2023
• University of Padova, Dec. 13-17, 2022