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.
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.
Seismic Imaging, Sensitivity Analysis, Inverse Problems, Groundwater Flow Modeling, Parameter Estimation, Numerical Analysis, Frechét Derivatives.
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.
Knot invariants and 3-manifold invariants, applications of topology to biology, recursion theory.
General theory of relativity, differential geometry, quantum gravity, Ricci flow.
Interdisciplinary within dynamical systems and algebraic and differential geometry with 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
Relativistic cosmology, differential geometry. Exact solutions of Einstein's Field Equations and Embedding Problems of Compact 3-Manifolds.
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.
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.
Statistical science, probability theory, stochastic processes, and related mathematics. Special focus on multivariate analysis, nonparametric methods, functional data analysis, outlier detection, time series, heavy tailed distributions, and asymptotic methods. Current special interest in applications to actuarial science, finance, biostatistics, bioinformatics, and robotics.
Statistical inference, nonparametric methods, confidence bands problems, time-series analysis, probability theory.
- Updated: February 6, 2006