Fall 2023
Joel Lebowitz
Subtitle:
Kinetic Equations
Course description:
We will study the derivation, solution and applications of macroscopic kinetic equations.
These include the diffusion equation, the Boltzmann equation, the Fokker-Planck equation, etc.
I will also discuss more microscopic stochastic time evolutions both classical and quantum.
Textbook:
None
Prereq:
Prerequisites are talking with instructor.
****************************
Spring 2023
A. Shadi Tahvildar-Zadeh
Subtitle:
Introduction to Relativistic Quantum Mechanics
Course description:
This will be an introduction to Special- and General-Relativistic Quantum Mechanics. A selection of the following topics will be covered: 1. Dirac's equation on curved backgrounds: self-adjointness, spectral analysis - 2. Quantum laws of motion for singularities of spacetime - 3. Interacting photon-electron systems - 4. Least-invasive quantization
Textbook:
None
Prereq:
Permission of instructor
****************************
Fall 2022
Avy Soffer
Subtitle:
Recent Developments in Scattering Theory
Course description:
This course will be to introduce a new approach being developed to mathematical scattering theory. The first part will be focused on basic facts from Functional Analysis, in particular the Spectral Theorem for general self-adjoint operators. This is then related to the basics of Quantum Mechanics and PDE's in general, via a quick introduction to QM. Next the basic notions of scattering theory are explained, and then the new approach is developed by solving the simple case of one body scattering. This is followed by extensions and new results for general Nonlinear Dispersive and Hyperbolic Equations. New open problems and new directions of research will be outlined.
Textbook:
Functional Analysis I, by M. Reed & B. Simon
Prereq:
Linear Algebra, Real Analysis
****************************
Spring 2022
A. Shadi Tahvildar-Zadeh
Subtitle:
Introduction to Relativistic Quantum Mechanics
Course description:
This will be an introduction to Special- and General-Relativistic Quantum Mechanics. A selection of the following topics will be covered: 1. Dirac's equation on curved backgrounds: self-adjointness, spectral analysis - 2. Quantum laws of motion for singularities of spacetime - 3. Interacting photon-electron systems - 4. Least-invasive quantization
Textbook:
None
Prereq:
517 & 661 or permission of instructor
****************************
Spring 2021 - A. Shadi Tahvildar-Zadeh
Subtitle:
Introduction to Mathematical Relativity II
Course description:
(Continuation of fall semester course: Intro. to Mathematical Relativity I) - Special- and General-Relativistic Quantum Mechanics: 1. Dirac's equation on curved backgrounds: self-adjointness, spectral analysis - 2. Quantum laws of motion for singularities of spacetime - 3. Interacting photon-electron systems - 3. Interacting photon-electron systems - 4. Least-invasive quantization
Textbook:
None
Prereq:
517 & 661 or permission of instructor
Schedule of Sections:
Previous Semesters:
- Spring 2020 Prof. Tahvildar-Zadeh
- Spring 2019 Prof. Kiessling
