SiMP

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.

Fall 2025:

  • This semester, we’re focusing on the dynamics of many-body classical systems and the derivation of kinetic models. Weekly meetings on Tuesdays 3:30-5:30pm, MB216. An organizational meeting on 08/26.
  • Tentative Schedule: 
    Date Speaker Topics Notes
    9/2 Toan Hard sphere dynamics after Deng-Hani-Ma Notes
    9/9 P. T. Nam Many body quantum systems Notes
    9/16 Felipe Fisher information for Landau
    9/23 T. Reid Cwikel’s bound reloaded
    9/30 Chanjin Landau consistency after Bobylev-Pulvirenti-Saffirio Notes
    10/7 E. Cardenas Derivation of effective dynamics for large quantum systems
    10/14 M. Rosenzweig Meanfield limit with singular potentials
    10/21 Peter M Fisher information for Boltzmann
    10/28 Junhwa Kac model after Paul-Pulvirenti-Simonella
    11/4 Nguyen Bogoliubov spectrum for Bose gases
    11/11 Marker lectures week
    11/18 Feiyang Pickl’s approach to meanfield Notes
    12/2 W. Schlag Semilinear Klein-Gordon equations
    12/9 Toan DHM papers in morning class (info below)

Spring 2025:

  • This semester I teach Graduate PDE 2, TR 1:35-2:50pm, MB216. My plan is to prepare the students some basic functional tools, analysis, and cover selected topics in PDEs (e.g. problems in fluid dynamics, plasma physics, quantum mechanics), as the semester progresses:
    • Introduction to PDEs in the physical theories.
    • Theory of distributions, Fourier transform, Sobolev embeddings.
    • Littlewood-Paley theory, Calderon-Zygmund theory.
    • Generators functions (e.g., Cauchy-Kovalevskaya theorem).
    • to be updated.
  • I will also write blog articles for Snapshots in Mathematics!

Fall 2024:

  • Weekly meetings on Thursdays 1-3pm, McAllister 216. We focus on going over works on derivation of Boltzmann equations, focusing especially the recent preprint by Deng-Hani-Ma (2024).
  • Tentative Schedule:
    Date Speaker Topics Notes
    9/5 Toan Lanford’s theorem
    9/12 Yuri Modified dynamics and correlations
    9/19 Joe Miller Boltzmann Hierarchy
    9/26 Yuri Clusters and cumulants
    10/3 Chanjin Proof of cumulant formulas
    10/10 Feiyang Reduction to spacetime integral
    10/17 Izabella Molecule operations
    10/24 Toan Reduction to combinatorics
    10/31 Ata Combinatoric bounds
    11/7 Yu Deng Cutting algorithm
    11/14 Chanjin Boltzmann approximation
    11/21 Yuri + Toan Other collisional models
    12/5
  • Some references:

Spring 2024:

 

Fall 2023:

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.

Fall 2022:

Spring 2022:

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).

 

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