The research of the Optimization group covers a wide range of topics, such as convex and variational analysis, semidefinite programming, convex and nonconvex programming, complementarity problems and variational inequalities, integer programming, and optimal control. By exploiting the fundamental structure in optimization problems, we have developed new computational and analytical methods and brought new insights into important classes of problems. We have also applied optimization techniques in a broad range of areas, including engineering, economics, physical, chemical, and biological sciences, business and management, data science and machine learning, transportation science, and social sciences.
The Probability group encompasses a wide range of research interests and research expertise including, Extreme Value Theory and stochastic dynamical systems with applications in Engineering, Oceanographic, Environmental and Biomedical sciences; Stochastic Analysis, Large Deviations and Stochastic Control, Markov processes and their applications; generalized fiducial inference and applications to biology and engineering; long range dependence and self-similarity; limits of random combinatorial structures including random graphs and random network models, dynamics on and off networks; evolutionary games and applications in mathematical biology, computer science and theoretical machine learning.
The research interests and expertise of the Statistics group encompass many active areas of statistical research and application, including inference for complex data, time series, and dynamical systems, machine learning, network analysis, environmental statistics, statistical genomics, and financial statistics. Group members are engaged in basic theory, the development of new statistical methods, and the creation of statistical software. Members of the Statistics group have developed methodology in collaboration with researchers in a number of fields, including genetics, genomics, medical imaging, biology, biomedicine, social sciences, and bioinformatics.
The Stochastic Modeling group mainly focuses on decision making under uncertainty in complex, dynamic systems, and emphasizes practical relevance. Standard stochastic methodological and modeling techniques like discrete and continuous-time Markov chains, renewal and regenerative processes, Markov decision processes, diffusion processes, optimal control theory, queueing theory, discrete-event simulation, and Monte Carlo simulation are heavily used but most research projects, particularly those of interdisciplinary nature, necessitate careful integration of these techniques with methods from statistics, forecasting, machine learning, et cetera, deterministic optimization, integer programming, convex optimization, et cetera, and economics, game theory, decision theory, et cetera.