-
Air Quality and Aerosol Dynamics Modeling
Associated Faculty
-
Applied Mathematics
Associated Faculty
-
Applied Partial Differential Equations
Modeling and analysis using partial differential equations tools and theories to study real-world 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, large-scale structure.
Associated Faculty
-
Bayesian Asymptotics
Broadly study the asymptotics of Bayesian models - characterizing theoretical properties of Bayesian mixture models, Bayesian high-dimensional semiparametric models and the asymptotics of Bayesian high-dimensional covariance/precision matrices estimation.
Associated Faculty
-
Bayesian Nonparametrics
Bayesian nonparametric modeling for high-dimensional 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
-
Causal Discovery
Associated Faculty
-
Climate Change
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, point-process 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 high-throughput techniques.
Associated Faculty
-
Environmental Statistics
Methods to assess uncertainty in environmental systems, with applications ranging from climate change to renewable energies.
Associated Faculty
-
Functional and Object Data Analysis
Associated Faculty
-
Geometry and Statistics
Associated Faculty
-
Geospatial Informatics
The use of data-rich maps to study public health issues
Associated Faculty
-
Graphical Models
Associated Faculty
-
High-Dimensional Statistical Inference
Associated Faculty
-
High-Dimensional Statistics
Associated Faculty
-
High-performance Computing
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 large-scale 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
-
Remote Sensing
Associated Faculty
-
Scientific Computing
The construction and implementation of mathematical algorithms to run on large parallel high-performance computers and their application to problems in science, engineering, and social science.
Associated Faculty
-
Spatio-temporal 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, cross-validation, stability, data splits, clustering, regularization, rates of convergence, mini-max theory, optimization, text analysis.
Associated Faculty
-
Systems Biology
Associated Faculty
-
Tensor Data Analysis
Associated Faculty
-
Time Series Analysis
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
-
Weather Research and Forecasting
Associated Faculty
-
Wind Energy
Associated Faculty