Summer Graduate School

This summer school will focus on the introductory notions related to the passage of Newtonian and quantum many-body dynamics to kinetic collisional models of Boltzmann flow models arising in statistical sciences in connection to model reductions when continuum macro dynamics arises; and their numerical schemes associated to transport of kinetic processes in classical and data driven mean field dynamics incorporating recent tools from computational kinetics and data science tools. There will be two sets of lectures: “From Newton to Boltzmann to Fluid dynamics”, and “Kinetic collisional theory in mean field regimes: analysis, discrete approximations, and applications”. Each lecture series will be accompanied by a collaboration session, led by the lecturer and teaching assistants. The purpose of the collaboration sessions is to encourage and strengthen higher-level thinking of the materials taught in the lectures and to direct further reading for interested students. Interactive learning activities will be conducted. For example, students will be given problem sets associated with the lectures and will work in small groups to discuss concepts and/or find solutions to assigned problems. The students will also be encouraged to give oral or poster presentations on their solutions or other materials relevant to the course.

There will be two sets of lectures:

• From Newton to Boltzmann to Fluid dynamics
• Kinetic collisional theory in mean field regimes: analysis, discrete approximations, and applications

This school will serve as an introduction to the semester program “Kinetic theory: Novel statistical, stochastic and analytical methods”.

School Structure

There will be two lectures each day, as well as two problem sessions.

Bibliography

Prerequisites

A good background in first year graduate real and functional analysis tools, basic graduate measure theory and probability methods, as well as basic notion of numerical analysis tools, such of those from Prelim graduate school courses in American institutions. A basic course of PDEs, graduate or even undergraduate, is recommended. This course is targeted to graduate students in Mathematics and Applied Computational Engineering, Science and Mathematics programs.

Application Procedure

For eligibility and how to apply, see the Summer Graduate Schools homepage.