Modeling, Simulation, and Optimization
of discrete, continuous and stochastic systems
Numerical and qualitative analysis of dynamical systems
Nonlinear and combinatorial optimization
Extremal discrete structures
Bayesian spatio-temporal prediction and design
Mathematical models of systems, e.g. in modern Information Technology, quite often exhibit both discrete and continuous aspects as well as their interaction. This concerns the modeling of time in dynamical systems either as a continuum or a finite/countable number of instances when observations are taken or when control acts, and strongly influences the analysis of the qualitative behavior of such systems as well as their design via continuous or combinatorial optimization methods, respectively. Moreover, robustness with respect to uncertainty caused by noise or perturbations is a crucial issue in such systems and needs skillful stochastic modeling as well as estimation, prediction and model validation. The rigorous and efficient treatment of these problems requires knowledge from a wide range of mathematical fields, namely Dynamical Systems, Statistical Data Analysis, Nonlinear and Combinatorial Optimization, Discrete Mathematics and Inverse Problems.
The aim of the MSO Doctoral Program is to provide PhD students with a combined training in these areas and thus enable them to successfully contribute to the development of new groundbreaking mathematical methods. Not only will these methods be applicable to the challenging problems of Information Technology investigated at our university, but they will also help to tackle a wide range of discrete-continuous-stochastic problems in Engineering as well as Natural, Economic and Social Sciences.
The research within the MSO Doctoral Program is driven by applications in Information Technology, in particular control and sensor/actuator technology, where the requirement of intimate cooperation between experts on differential equations, optimization and stochastics becomes most evident.