# 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

#### 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

###### Associate Research Professor of Mathematics

**Keywords in this area**

topological data analysis, data science

#### 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

#### John Harer

###### Professor of Mathematics

**Keywords in this area**

Topological Data Analysis,
Geometric Data Analysis,
Network Dynamics,
Network Inference

#### Gregory Joseph Herschlag

###### Assistant Research Professor of Mathematics

**Keywords in this area**

physical modeling, kinetic equations, surface catalysis, molecular dynamics, stochastic boundary conditions

#### Anita T. Layton

###### Research 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

#### 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

###### James B. Duke Professor

**Keywords in this area**

Markov Chain Mixing, Stochastic Numerical Methods, High Dimensional Random Algorithms

#### Amanda Randles

###### Alfred Winborne and Victoria Stover Mordecai Assistant Professor of Biomedical Sciences

#### Thomas P. Witelski

###### Professor in the Department of Mathematics

**Keywords in this area**

numerical partial differential equations