General theory of relativity, differential geometry, quantum gravity, Ricci flow.
Robust multivariate statistical methods, signal processing, statistical computing, applied probability, remote sensing.
Asymptotic dynamics of large ensembles of particles, switching Hamiltonian systems, fluid dynamics.
Nonlinear analysis (equivariant degree), dynamical systems with symmetries (bifurcation theory), mathematical theory of hysteresis, non-associative algebras.
Sequential analysis, change-point problems, sequential methods in clinical trials, epidemiology, and finance.
Biostatistics, Statistical Genetics, Genetic Epidemiology, Cancer Genetics, Risk Prediction Models, Bayesian Clinical Trials.
Medical image analysis, computational anatomy, computer vision, pattern theory, shape analysis and shape models.
U-Statistics, Nonparametric Methods, Applied Sequential Methods, Spatio-Temporal Modeling.
Genome wide association studies; eQTL mapping; Network based modeling; Next generation sequencing data analysis; Statistical preprocessing of genomic data; Cancer genetics/epigenetics; Integrative/meta analysis; Spatial modeling; Model selection; Ranked set sampling.
Biostatistical inference, Statistical methodology, Method comparison studies.
Knot invariants and 3-manifold invariants, applications of topology to biology, recursion theory.
Actuarial science, business analytics, economic decision analysis, multi-objective optimization decision problems under constraints using statistical simulation techniques, statistical analysis of discrete event modeling and simulation.
Integrable Dynamical Systems, Algebraic and Differential Geometry, applications to Classical and Statistical Mechanics.
Information theory, optimization, probability, statistical inference, nonparametric curve estimation, time series analysis.
Time series analysis, spatio-temporal processes, regularization for weakly dependent data, high-dimensional inference, statistical inference for random graphs and networks, nonparametrics, bootstrap and resampling. Applications of statistics to environmental modeling, epidemiology, finance and legal studies.
Scattering theory, inverse scattering theory with geophysical and optical applications, fission.
Dynamical systems; state-dependent delay differential equations and their applications in engineering and biology; equivariant degree theory and applications; nonlinear analysis; operations research.
Actuarial science, applied complex variable analysis, probability.
Nonparametric statistics, ranking procedures in factorial designs, multiple testing problems, resampling techniques, Biostatistics.
Topological methods in nonlinear analysis, symmetric differential equations and bifurcation problems.
Compressive sensing and its applications, Image analysis (medical imaging, hyperspectral, imaging through turbulence), numerical analysis and optimization algorithms.
General research areas:
Actuarial science, statistics, assets and liabilities management, and experience study of insurance portfolio.
Statistical modeling of insurance portfolio, mathematics of financial instruments, and experience study of financial instruments.
Nonsmooth dynamical systems, Moreau's sweeping processes, dispersing billiards, switching closed-loop control: oscillations, stability, bifurcations, regularization. Non-monotone population models.
Scientific computing with primary emphasis to date on numerical modeling for geoscience problems (seismic imaging and wave propagation, reservoir simulation, and mechanical deformation modeling). Mathematics and numerical simulation to model the "real-world" as closely as possible given limitations in physics, mathematics, and computer science. Broad interests include not only earth science, but almost all physical,chemical, and biological problems that can benefit from the skills and insights of an applied mathematician.
Applications of differential geometry to problems in physics and engineering, particularly those problems described as Hamiltonian dynamical systems in a broad sense. They include semiclassical and quantum dynamics, nonholonomic dynamics, and optimal control theory.
Mathematical modeling and numerical simulation of multiphase flows in porous media at the field, laboratory, and pore scales; Uncertainty quantification methods for applications related to CO2 storage, oil recovery, and contaminant transport; Pore network construction algorithms; Numerical methods for partial differential equations; High performance, parallel, scientific computing.
Dynamical systems and systems with hysteresis, nonlinear analysis, applied mathematical modeling.
Control, optimization, computation, applications in material and molecular sciences.
General relativity theory, particularly exact solutions to Einstein's equations of gravitation. Gravitational radiation and the geometry of the null paths along which protons and gravitrons travel. He is currently working on twisting gravitational waves and on some applications of Clifford Algebra.
Statistical science, probability theory, stochastic processes, biostatistics, and related mathematics. Special focus on multivariate quantile and rank methods, nonparametric methods, functional data analysis, outlier detection, heavy tailed time series, asymptotic methods, and probability modeling for interpretation of prostate cancer biopsy results.
Statistical inference, nonparametric methods, confidence bands problems, time-series analysis, probability theory.
Quantum Topology and Knot Theory. I am particularly interested in the Jones polynomial, skein modules, character varieties, the A-polynomial, the Alexander polynomial, and left-orderability of fundamental groups.
Functional differential equations, integral equations, approximation theory, optimal control theory, numerical analysis, applied functional analysis.
Robust linear models, statistical classification, multivariate analysis, applications of statistics to the physical and medical sciences.
Multiscale modeling and simulation of subsurface flows in porous media. Parallel implementation of numerical methods for partial differential equations.
Modeling, analysis, simulation, experimental validation, and design optimization of high performance optical systems and devices; Image analysis and applications of differential geometry.
- Updated: September 15, 2015