Numerical linear algebra and high-performance computing, low-rank matrix and tensor techniques, computational differential geometry, eigenvalue problems, high-performance computing, and model reduction.
Numerical analysis and computational mathematics, modeling and numerical analysis of multiscale partial differential equations, numerical methods for atomistic simulation, numerical methods for stiff and stochastic differential equations.
Statistical methodology, causal inference, survival analysis, longitudinal data analysis epidemiologic methods, mediation analysis, randomized experiments
Mathematical physics, probability, statistical mechanics, field theories, conformal symmetry, complex analysis, lattice models, exactly solvable models, neural networks.
Numerical Analysis of PDEs, parallel computing, reduced order modeling. Applications to the simulaiton of the Cardio-vascular system.
My general research interests concern nonlinear mechanics and mathematics, with emphases on i) parameter continuation, bifurcation and stability exchange results, ii) variational principles.
High-order and spectral methods for PDEs, Numerical analysis for time-dependent PDEs, Reduced order methods, Computational wave problems, Machine learning in scientific applications, High performance and parallel computing, Computational science and engineering.
Fundamental limits and algorithms for data processing and machine learning. Statistics, discrete probability, learning theory, information theory, algorithms.
Theory and applications of optimization in continuous variables, with a focus on geometry and non-convexity; aspects of numerical analysis and statistical estimation through the lens of optimization and geometry.
Statistics for big and heterogeneous data sets. Analysis of time series, random fields and point processes. Statistics of network data. Ethics of data science.
Development of statistical methodology, investigation of probability models and analysis of data that arise in natural sciences.