Computational Mathematics

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 efficient numerical methods for solving physical or biological models, analysis of numerical approximations to differential and integral equations, developing computational tools to better understand data and structure, etc. Computational mathematics is a field closely connected with a variety of other mathematical branches, as for often times a better mathematical understanding of the problem leads to innovative numerical techniques.

Duke's Mathematics Department has a large group of mathematicians whose research involves scientific computing, numerical analysis, machine learning, computational topology, and algorithmic algebraic geometry. The computational mathematics research of our faculty has applications in data analysis and signal processing, fluid and solid mechanics, electronic structure theory, biological networks, and many other topics.

Faculty

Pankaj K. Agarwal

RJR Nabisco Professor of Computer Science in Trinity College of Arts and Sciences

William K. Allard

Professor Emeritus of Mathematics

Keywords in this area
Multiresolution Geometrical Analysis

J. Thomas Beale

Professor Emeritus of Mathematics

Keywords in this area
boundary integral methods, computation of singular and nearly singular integrals, maximum norm estimates for finite difference methods, convergence of numerical methods for fluid flow

Paul L Bendich

Assistant Research Professor in the Department of Mathematics

Keywords in this area
topological data analysis, data science

Robert Bryant

Philip Griffiths Professor of Mathematics

Keywords in this area
integrability

Robert Calderbank

Charles S. Sydnor Professor of Computer Science

Keywords in this area
discrete harmonic analysis, algorithms

Ingrid Daubechies

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

Keywords in this area
inverse problems

Tingran Gao

Visiting Assistant Professor in the Department of Mathematics

Keywords in this area
Algorithms, Applied Harmonic Analysis, Multi-scale Analysis

John Harer

Professor of Mathematics

Keywords in this area
Topological Data Analysis, Geometric Data Analysis, Network Dynamics, Network Inference

Gregory Joseph Herschlag

Visiting Assistant Professor of Mathematics

Keywords in this area
physical modeling, kinetic equations, surface catalysis, molecular dynamics, stochastic boundary conditions

Anita T. Layton

Robert R. & Katherine B. Penn Professor of Mathematics

Keywords in this area
mathematical biology, mathematical physiology, mathematical modeling, kidney physiology, renal hemodynamics, diabetes, multiscale modeling, fluid-structure interactions, computational fluid dynamics, numerical partial differential equations, feedback control, systems biology

Jian-Guo Liu

Professor of Physics

Jianfeng Lu

Associate Professor of Mathematics

Keywords in this area
electronic structure models, multiscale modeling and simulations, numerical analysis, rare events simulation, computational physics, time-frequency analysis, fast algorithms, stochastic numerical methods, kinetic equations, nonlinear Schrodinger equations, quantum chemistry, computational statistical mechanics, optimization, high frequency wave propagation

Mauro Maggioni

Research Professor of Mathematics

Keywords in this area
statistical learning, machine learning, signal processing, algorithms

Jonathan Christopher Mattingly

Professor of Mathematics

Keywords in this area
Markov Chain Mixing, Stochastic Numerical Methods, High Dimensional Random Algorithms

missing portrait

Marc Ryser

Visiting Scholar (Affiliate Position)

Keywords in this area
cancer evolution

Thomas Peter Witelski

Professor in the Department of Mathematics

Keywords in this area
numerical partial differential equations

Haizhao Yang

Visiting Assistant Professor in the Department of Mathematics

Keywords in this area
High performance scientific computing, fast algorithms, numerical linear algebra, computational materials science

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, kinetic theory, Born-Oppenheimer approximation, numerical methods for conservation law