Research Areas

  • 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

  • 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

  • Geometry and Statistics

    Associated Faculty

  • Geospatial Informatics

    The use of data-rich 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 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

  • 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

  • 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