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.
Information theory, optimization, probability, statistical inference, nonparametric curve estimation, time series analysis.
Actuarial science, applied complex variable analysis, probability.
Nonlinear analysis (equivariant degree), dynamical systems with symmetries (bifurcation theory), mathematical theory of hysteresis, non-associative algebras.
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.
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.
Nonsmooth dynamical systems, Moreau's sweeping processes, dispersing billiards, switching closed-loop control: oscillations, stability, bifurcations, regularization. Non-monotone population models.
Numerical Analysis and Scientific Computing.
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.
Nonlinear PDEs that model optical systems, Bose-Einstein condensates and plasma. Methods employed include asymptotics, variational approximations, rigorous analysis, numerical analysis and scientific computing.
Functional differential equations, integral equations, approximation theory, optimal control theory, numerical analysis, applied functional analysis.
Modeling, analysis, simulation, experimental validation, and design optimization of high performance optical systems and devices; Image analysis and applications of differential geometry.
Medical image analysis, computational anatomy, computer vision, pattern theory, shape analysis and shape models.
General theory of relativity, differential geometry, quantum gravity, Ricci flow.
Asymptotic dynamics of large ensembles of particles, switching Hamiltonian systems, fluid dynamics.
Knot invariants and 3-manifold invariants, applications of topology to biology, recursion theory.
Integrable Dynamical Systems, Algebraic and Differential Geometry, applications to Classical and Statistical Mechanics.
Analytical, numerical and experimental methods of fluid (plasma) mechanics.
Quantum topology, quantum computing, knot theory, category theory, quantum logic.
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.
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.
Robust multivariate statistical methods, signal processing, statistical computing, applied probability, remote sensing.
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.
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.
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.
Nonparametric statistics, ranking procedures in factorial designs, multiple testing problems, resampling techniques, Biostatistics.
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.
- Updated: July 20, 2015