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.
- PDE Seminar.
Spring 2024:
- Weekly meetings on Tuesdays MB216 3-5pm. We focus on reviewing works on many body quantum problems.
- Tentative Schedule:
Date Speaker Topics Notes 1/30 Toan Overview on the subject Lewin lectures, Rougerie survey, Benedikter at al. review 2/6 Izabella Stuhl BEC for ideal gases Some further references: Lieb-Seiringer, Brennecke at al. (for interacting gases) 2/13 Yuri Soukhov Thermodynamic limits 2/20 Fei Yang Phase transition Slides 2/27 Chanjin You Asymptotic completeness I 3/12 Chanjin You Asymptotic completeness II J. Derezinski, Ann Math ’93 3/19 Toan Uniqueness of BBGKY hierarchy Klainerman-Machedon ’08 3/21 Justin Holmer A derivation of quantum Boltzmann Thursday 10-noon, MB216
- Some suggested references:
Fall 2023:
- Weekly meetings on Thursdays MB216 10:30am-12:30pm to go over the recent series of implosion solutions to fluid equations by Merle-Raphael-Rodnianski-
Szeftel. - Main presenters: Chanjin You, Kieran Cavanagh, Alain Blaustein.
- a lecture by Jia Shi (MIT) on her recent work on non-radial implosion solutions, Oct 25.
- a lecture by Kris Jenssen on Lazarus’s paper, Nov 3.
Spring 2023:
- Weekly meetings to review the question of global regularity for Vlasov-Maxwell systems and Hartree equations after Glassey-Schaeffer, Glassey-Strauss, Klainerman-Staffilani, and after Lewin-Sabin, respectively.
- Main presenters: Chanjin You, Kieran Cavanagh.
Fall 2022:
- 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
Spring 2022:
- This semester, I teach the PDE graduate course and organize the PDE Seminar.
Fall 2021:
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- 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:
Date Speaker Topics 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 (Trinh Nguyen on Bogoliubov theory; Fengyuan Zhang on ground state energy)
- 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.
Old slides: