1) Combinatorial Optimization. We investigate complex discrete optimization problems that arise at the interface of operations research, applied mathematics, and theoretical computer science. A primary goal is to design (exact, approximate, and heuristic) algorithms to solve such problems. The development of such algorithms heavily exploits advanced techniques in the areas of mathematical programming, polyhedral combinatorics, graph theory and network design. Typical application areas are scheduling, production planning, logistics, telecommunication/routing networks, game theory, health care, data science.
2) Stochastic Operations Research. We study the effects of randomness and uncertainty on complex systems and optimization problems, with techniques at the intersection of applied probability and operations research. Particular attention is given to the area of stochastic processes on interacting networks, queueing theory and the analysis of random walks and higher-dimensional Markov processes. A key goal is to develop analytic, probabilistic, algorithmic and asymptotic methods, with emphasis on asymptotic laws and scaling limits for large-scale critical systems. Typical application areas are computer-communications, energy networks, logistics and service operations, biological systems, particle interactions, and social networks.
3) Probability. We investigate probabilistic networks and their applications in statistical physics and networking. A special focus is on the structure of random graphs, algorithms and stochastic processes on them, as well as spin systems and self-interacting random processes. The main aim is to identify the scaling behavior for such systems, by applying methodology such as large deviations, combinatorial expansions and coupling techniques. Applications include physics, social networks, and complexity problems such as arising in chemistry and biomedical engineering.
4) Statistics. We develop and compare data-analytical methods for analyzing and sampling complex structured correlated data sets. It includes parameter estimation, model fitting, latent variable models, mixed models, missing data, statistical process control, survival and reliability theory, time series analysis, and statistical learning methods. One of the central themes is the analysis of high-dimensional temporal data sets and other large data sets. Applications include data science and machine learning, biopharmaceutical companies, chemical industry, medical centers.