Ranked in the top 20 math graduate programs by U.S. News & World Report, our faculty conduct more than $3.7 million in research each year for industry, the Department of Defense, the National Science Foundation, and the National Institutes of Health. Our faculty of 35 includes three National Academy of Science members and two National Academy of Engineering members. The Department supports more than 50 graduate students.

# Research

## Research Areas

Algebra refers to the use and manipulation of symbols, often with each representing some mathematical entity such as a quantity (think integer or real number), a set with special structure (think... Read more about Algebra and Combinatorics »

Functions are representations of relations between sets, and in particular are useful for representing the changing states of a system: the velocity of a projectile, the frequencies present in a... Read more about Analysis »

In recent decades, an explosive synergy between biology and mathematics has greatly enriched and extended both fields. Indeed, given its ability to reveal otherwise invisible worlds in all kinds of... Read more about Biological Modeling »

Computational Mathematics involves mathematical research in areas of science and engineering where computing plays a central and essential role. Topics include for example developing accurate and... Read more about Computational Mathematics »

Researchers at Duke use geometric methods to study: the geometry and arithmetic of algebraic varieties; the geometry of singularities; general relativity and gravitational lensing exterior... Read more about Geometry: Differential & Algebraic »

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... Read more about Mathematical Physics »

Number theory is the study of the integers (i.e. whole numbers) and related objects. Topics studied by number theorists include the problem of determining the distribution of prime numbers within the... Read more about Number Theory »

Partial differential equations (PDEs) are one of the most fundamental tools for describing continuum phenomena in the sciences and engineering. Early work on PDEs, in the 1700s, was motivated by... Read more about PDE & Dynamical Systems »

Mathematical research in physical modeling focuses on the formulation and analysis of mathematical representations of problems motivated by other branches of science and engineering. In addition to... Read more about Physical Modeling »

Probability and Stochastic process is the study of randomness. It is at once a theoretical and abstract subject and one which is highly applied. Probability is both an increasingly core subject in... Read more about Probability »

A large number of signals is collected from a wide variety of physical and biological phenomena, and in a variety of forms, ranging from acoustics, radar, camera images, hyper-spectral images, movies... Read more about Signals, Images, and Data »

Topology is the study of shapes and spaces. What happens if one allows geometric objects to be stretched or squeezed but not broken? In fact there’s quite a bit of structure in what remains, which is... Read more about Topology »