# Mathematical Physics

Mathematical physics seeks to apply rigorous mathematical ideas to problems in physics, or problems inspired by physics. As such, it is a remarkably broad subject. Mathematics and Physics are traditionally very closely linked subjects. Indeed historical figures such as Newton and Gauss are difficult to classify as purely physicists or mathematicians. Traditionally mathematical physics has been quite closely associated to ideas in calculus, particularly those of differential equations. In recent years however, in part due to the rise of superstring theory, there has been a great enlargement of branches of mathematics which can now be categorized as part of mathematical physics. It is often joked that, in additional to unifying all of physics, superstring theory also encompasses all of mathematics!

At Duke, the mathematical physics studied is related to geometrical ideas. Hugh Bray and Arlie Petters both study gravity and general relativity. The involves techniques from differential geometry. Hugh Bray is particularly interested in models of dark matter, which makes up most of the mass of galaxies. Current research topics also involve black holes and theoretical considerations behind gravitational waves. Arlie Petters studies how gravity acts on light. His work includes applications of gravitational lensing to astronomy and astrophysics, which is one of leading observational techniques in the modern study of dark matter and black holes.

As well as differential geometry, the subject of algebraic geometry now has many applications in mathematical physics. Paul Aspinwall is a string theorist who specializes in using techniques from algebraic geometry to study the higher-dimensional spaces that abound in the subject. This includes the subject of compactification, which makes the ten-dimensional universe, predicted by string theory, appear to us as a four dimensional spacetime.

## Faculty

#### Paul Stephen Aspinwall

###### Professor of Mathematics

**Keywords in this area**

String Theory, Compactification, D-Brane Categories.

#### Hubert Bray

###### Professor of Mathematics

**Keywords in this area**

black holes, Einstein curvature, general relativity, quasi-local mass, dark matter, galactic curvature

#### Robert Bryant

###### Philip Griffiths Professor of Mathematics

**Keywords in this area**

holonomy, exterior differential systems, symplectic geometry

#### Ingrid Daubechies

###### James B. Duke Professor of Mathematics and Electrical and Computer Engineering

**Keywords in this area**

time-frequency analysis

#### Goncalo Marques Fernandes de Oliveira

###### William W. Elliott Assistant Research Professor

**Keywords in this area**

Gauge theory

#### Jianfeng Lu

###### Associate Professor of Mathematics

**Keywords in this area**

electronic structure models, quantum chemistry, kinetic theory, quantum information

#### Arlie O. Petters

###### Benjamin Powell Professor of Mathematics in Trinity College of Arts and Sciences

**Keywords in this area**

gravity, light, geometric lensing, stochastic lensing, black holes, extra dimensions, singularities

#### Mark A. Stern

###### Professor of Mathematics

**Keywords in this area**

Yang Mills theory, String theory

#### Zhennan Zhou

###### William W. Elliott Assistant Research Professor

**Keywords in this area**

semi-classical methods in quantum dynamics, multi-scale methods for physics models, band crossing for Bloch electrons, Born-Oppenheimer approximation