Computational Mathematics

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

Pankaj K. Agarwal

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

William K. Allard

William K. Allard

Professor Emeritus of Mathematics

Keywords in this area
Multiresolution Geometrical Analysis

J. Thomas Beale

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

Paul L Bendich

Associate Research Professor of Mathematics

Keywords in this area
topological data analysis, data science

Robert Bryant

Robert Bryant

Phillip Griffiths Professor of Mathematics

Keywords in this area
integrability

Robert Calderbank

Robert Calderbank

Charles S. Sydnor Professor of Computer Science

Keywords in this area
discrete harmonic analysis, algorithms

Xiuyuan Cheng

Xiuyuan Cheng

Assistant Professor of Mathematics

Ingrid Daubechies

Ingrid Daubechies

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

Keywords in this area
inverse problems

John Harer

John Harer

Professor of Mathematics

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

Gregory Joseph Herschlag

Gregory Joseph Herschlag

Phillip Griffiths Assistant Research Professor

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

Anita T. Layton

Anita T. Layton

Professor in the Department 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

Jian-Guo Liu

Professor of Physics

Jianfeng Lu

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

Jonathan Christopher Mattingly

Jonathan Christopher Mattingly

Professor of Mathematics

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

Henry Pfister

Henry Pfister

Associate Professor in the Department of Electrical and Computer Engineering

Amanda Randles

Amanda Randles

Alfred Winborne and Victoria Stover Mordecai Assistant Professor of Biomedical Sciences

Marc Daniel Ryser

Marc Daniel Ryser

Assistant Professor in Population Health Sciences

Keywords in this area
cancer evolution

Guillermo Sapiro

Guillermo Sapiro

James B. Duke Professor of Electrical and Computer Engineering

Thomas Peter Witelski

Thomas Peter Witelski

Professor in the Department of Mathematics

Keywords in this area
numerical partial differential equations