Mathematical Physics and Partial Differential Equations

This project considers a number of problems from Mathematical Physics and Partial Differential Equations. In Mathematical Physics the overall goal is a rigorous mathematical understanding of the problems, and the selected problems have a number of common features. In Partial Differential Equations the goals include both the study of explicit problems, several of them arising from Mathematical Physics, and the development of new methods.

There is a range of common mathematical methods entering into the analysis of problems in Mathematical Physics and Partial Differential Equations. They include results and techniques from functional analysis, operator theory, and geometric analysis. Specific problems often require a wider range of techniques.

MATHEMATICAL PHYSICS, problems to consider:

Quantum systems in external fields.
Behavior of quantum systems at thresholds.
Quantum transport in mesoscopic systems.
Mathematical models for quasi-particles in nanoscopic systems.
Problems in many-body quantum mechanics
Atomic and molecular Hamiltonians.
Translation invariant models in Non-relativistic QED and solid state physics.
Quantum gravity

PARTIAL DIFFERENTIAL EQUATIONS, problems to consider:

Regularity questions
Geometric questions
Scattering theory for hyperbolic Laplacians