• 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.

Spring 2023:

• 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.

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:

• 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:

• Slides for Graduate Student Seminar on kinetic theory, 2017

• Slides for Graduate Student Seminar on fluids, 2018

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