# 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

###### Assistant Research Professor in the Department 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

#### 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

#### 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

#### Sayan Mukherjee

###### Professor in the Department of Statistical Science

**Keywords in this area**

machine learning

#### 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