
Applied Mathematics
Associated Faculty

Applied Partial Differential Equations
Modeling and analysis using partial differential equations tools and theories to study realworld problems arising from the natural and social sciences and engineering.
Associated Faculty

Applied Statistics
Associated Faculty

Astrostatistics
Statistical analysis of the Universe: galaxy morphologies, redshift, stars, quasars, largescale structure.
Associated Faculty

Bayesian Asymptotics
Broadly study the asymptotics of Bayesian models  characterizing theoretical properties of Bayesian mixture models, Bayesian highdimensional semiparametric models and the asymptotics of Bayesian highdimensional covariance/precision matrices estimation.
Associated Faculty

Bayesian Nonparametrics
Bayesian nonparametric modeling for highdimensional data, complex data or Big data; Bayesian asymptotics or large sample theory for Bayesian models
Associated Faculty

Bayesian Statistics
Development and application of Bayesian methodology towards data analysis and experimental designs, such as clinical trials, decision making, macrosystem biology, epidemiology modeling, and missing data.
Associated Faculty

Big Data Analysis
Develop robust and scalable models and algorithms for big data analysis with theoretical guarantees.
Associated Faculty

Bioinformatics and Biostatistics
The application of statistical and computational methods to biological and medical data to model, analyze, and predict biological processes.
Associated Faculty

Cancer Evolution
Associated Faculty

Computational Fluid Dynamics
Associated Faculty

Computational Mathematics
Associated Faculty

Computational Neuroscience
Mathematical and statistical models to explain the principles that govern the brain, from subcellular biophysics to behavior: differential equations, pointprocess models, graphical models, dimension reduction.
Associated Faculty

Computational Physics
The development and implementation of numerical methods to solve mathematical problems in physics.
Associated Faculty

Data Mining
Modeling, regression, classification, clustering, and testing on modern datasets, especially big datasets generated by highthroughput techniques.
Associated Faculty

Environmental Statistics
Methods to assess uncertainty in environmental systems, with applications ranging from climate change to renewable energies.
Associated Faculty

Geometry and Statistics
Associated Faculty

Geospatial Informatics
The use of datarich maps to study public health issues
Associated Faculty

Mathematical and Computational Biology
Multiscale modeling, using a combination of discrete stochastic systems and differential equations, of biomedical problems including blood clot formation, spread of infection, development, and cancer.
Associated Faculty

Mathematical Cell Biology
Associated Faculty

Mathematical Finance
Associated Faculty

Mathematical Modeling
Associated Faculty

Medical Image Processing
Development of computational approaches for image reconstruction and flow quantification in Magnetic Resonance and Ultrasound imaging
Associated Faculty

Network Analysis
Statistical network analysis for largescale networks; Bayesian network analysis; Development of central limit theorems for large collection of network objects.
Associated Faculty

Nonlinear Dynamics
Associated Faculty

Numerical Algebraic Geometry
The discovery, implementation, and application of algorithms to numerically compute and manipulate the solution sets of systems of polynomials.
Associated Faculty

Numerical Analysis
Associated Faculty

Numerical Solution of Differential Equations
The design, efficient implementation, and analysis of numerical methods for solving differential equations arising in science and engineering.
Associated Faculty

Pattern Formation
Associated Faculty

Probabilistic Graphical Models
Models describing the dependence structure of large numbers of random variables by means of graphs: undirected, directed, and dynamic. Applications: neuroscience, genomics, proteomics, metabolomics, sociology, economics, and several other fields.
Associated Faculty

Scientific Computing
The construction and implementation of mathematical algorithms to run on large parallel highperformance computers and their application to problems in science, engineering, and social science.
Associated Faculty

Spatiotemporal Statistics
Development of scalable methods for capturing dependence structure of data in space and time.
Associated Faculty

Statistical Machine Learning
Prediction, inference, parametric and nonparametric regression, classification, model selection, crossvalidation, stability, data splits, clustering, regularization, rates of convergence, minimax theory, optimization, text analysis.
Associated Faculty

Systems Biology
Associated Faculty

Topological Data Analysis
Statistical analysis of topological features of data, including persistent homology. Applications: astronomy, biomolecules, liver lesions, cortical thickness, autism, chemometrics, brain arteries, and networks.
Associated Faculty

Uncertainty Quantification
Development of efficient computational paradigms to propagate aleatoric and epistemic uncertainty through computational models
Associated Faculty