### Description

This NSF proposal concerns research in the deep relationships between solutions to partial

differential equations, differential geometry, dynamical systems, and mathematical physics.

These different areas of mathematics are often tied together by problems in spectral theory

and microlocal analysis; that is, problems concerned with eigenvalues, eigenfunctions, phase

space localization, and the generalizations thereof. The research in this proposal is divided

between selfadjoint and non-selfadjoint eigenfunction problems. Selfadjoint eigenfunction problems include eigenfunction scarring and non-concentration phenomena, quantum chaos, unique continuation properties, distribution of eigenvalues and resonances, and even waves in general relativity. Non-selfadjoint eigenfunction problems include damped waves, heat flow in inhomogeneous materials, statistical physics problems, predictive micro-fluidics, dialysis and many others.

differential equations, differential geometry, dynamical systems, and mathematical physics.

These different areas of mathematics are often tied together by problems in spectral theory

and microlocal analysis; that is, problems concerned with eigenvalues, eigenfunctions, phase

space localization, and the generalizations thereof. The research in this proposal is divided

between selfadjoint and non-selfadjoint eigenfunction problems. Selfadjoint eigenfunction problems include eigenfunction scarring and non-concentration phenomena, quantum chaos, unique continuation properties, distribution of eigenvalues and resonances, and even waves in general relativity. Non-selfadjoint eigenfunction problems include damped waves, heat flow in inhomogeneous materials, statistical physics problems, predictive micro-fluidics, dialysis and many others.

Status | Active |
---|---|

Effective start/end date | 9/1/15 → 8/31/18 |

### Funding

- National Science Foundation (NSF)

### Fingerprint

Qualitative Properties

Eigenfunctions

Microlocal Analysis

Eigenvalue

Quantum Chaos

Unique Continuation

Statistical Physics

Heat Flow

Microfluidics

Differential Geometry

General Relativity

Spectral Analysis

Damped

Phase Space

Dynamical system

Physics