Research Areas

Modeling and analysis using partial differential equations tools and theories to study real-world problems arising from the natural and social sciences and engineering.

Statistical analysis of the Universe: galaxy morphologies, redshift, stars, quasars, large-scale structure.

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.

Develop robust and scalable models and algorithms for big data analysis with theoretical guarantees.

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

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.

The development and implementation of numerical methods to solve mathematical problems in physics.

Modeling, regression, classification, clustering, and testing on modern datasets, especially big datasets generated by high-throughput techniques.

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

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.

Development of computational approaches for image reconstruction and flow quantification in Magnetic Resonance and Ultrasound imaging

Statistical network analysis for large-scale networks; Bayesian network analysis; Development of central limit theorems for large collection of network objects.

The discovery, implementation, and application of algorithms to numerically compute and manipulate the solution sets of systems of polynomials.

The design, efficient implementation, and analysis of numerical methods for solving differential equations arising in science and engineering.

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.

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.

Development of scalable methods for capturing dependence structure of data in space and time.

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.

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

Development of efficient computational paradigms to propagate aleatoric and epistemic uncertainty through computational models