Snapshots in Mathematical Physics Group
The goal of this group is to review some classical unsolved problems in physics and study recent mathematical progress on them. Of interest include fundamental problems in fluid dynamics, plasma physics, quantum mechanics, and general relativity. Activities include weekly meetings, presentations, and seminars to go over relevant materials. Contact me if you're interested in joining the group.
Weekly meetings on Tuesdays 2-4pm with continuation on Hartree-Fock and Vlasov models.
Weekly meetings on Thursdays 2-3pm with presentation out of Stein's oscillatory integrals book.
The PDE Seminar on Wednesdays 2:30-3:30pm.
Weekly meetings on Tuesdays 2-4pm with focus on the Hartree-Fock-Bogoliubov theory and the meanfield Vlasov models.
I teach the Graduate Dispersive PDEs and organize the PDE Seminar.
A new blog article on Dispersion for Schrodinger equations
This semester, I teach the PDE graduate course and organize the PDE Seminar.
The group will focus on problems in quantum mechanics, which meets weekly on Wednesdays 4-6pm, MB114 in person and via a zoom broadcast. The first meeting is on Aug 25th (organizational).
(Tentative) Presentation and lecture notes:
|Sep 1st||Toan||Overview on the subject||Slides and an old blog|
|Sep 15||Alex Vizcarra||Some physical background|
|Sep 22||Kieran Cavanagh||On the classical meanfield limit|
|Sep 29||Toan||Dispersion for meanfield equations||Blog|
|Oct 6||Chanjin You||I. Rodnianski and B. Schlein's paper|
|Oct 18||(Professor Benjamin Schlein's CAM colloquium)|
|Oct 27||Chanjin You||Convergence Towards Hartree Dynamics (after Rodnianski-Schlein)||Slides|
|Nov 3||Kieran Cavanagh||Golse's lecture notes (continued)|
|Nov 10||Toan||Strichartz estimates for Schrodinger equations|
|Nov 17||Toan||Scattering for nonlinear Schrodinger (e.g. Gross-Pitaevskii) equations|
Some suggested references:
R. Seiringer, Hot topics in cold gases, ICMP Proceedings, 2010
E. H. Lieb, R. Seiringer, J. Solovej, J. Yngvason, The Mathematics of the Bose Gas and its Condensation, Oberwolfach Seminars (book), 2005
M. Lewin, P. T. Nam, S. Serfaty, and J. Solovej, Bogoliubov spectrum of interacting Bose gases, CPAM 2015
H. Spohn, Kinetic equations from Hamiltonian dynamics: Markovian limits, Rev. Mod. Phys. 1980
F. Golse, On the Dynamics of Large Particle Systems in the Mean Field Limit, Lecture notes 2013
N. Rougerie, Scaling limits of bosonic ground states, from many-body to non-linear Schrodinger, EMS survey 2021
I. Rodnianski and B. Schlein, Quantum Fluctuations and Rate of Convergence towards Mean Field Dynamics, CMP 2009
L. Erdos, B. Schlein, H.T. Yau, Derivation of the cubic non-linear Schrodinger equation from quantum dynamics of many-body systems, Invent. Math 2007
L. Erdos, B. Schlein, H.T. Yau, Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate, Annals 2010
M. Lewin and J. Sabin, The Hartree equation for infinitely many particles, Anal PDE 2014 and CMP 2015. Also, CPDE 2020.
Back to Toan Nguyen's homepage.
Visit Toan Nguyen's blog: Snapshots in Mathematics!.