Research
Scientific Computation encompasses mathematical modeling, the design of numerical methods and algorithms as well as their implementation for problems from all areas of science and their applications. It also includes basic research on algorithms and complexity on the one hand and the design and implementation of software for scientific problems on the other hand.
Principal aim of the DFG Research Training Group is the development of efficient solution methods in the field of Scientific Computation, guided by different real world problems from science and engineering. In accordance with this aim, all research projects are interdisciplinary, with mathematics and computer science as basic fields, but with a strong component from engineering and the natural sciences.
In contrast to approaches in Scientific Computation where one seeks cooperation either between mathematicians and applied scientists or between computer scientists and applied scientists, the DFG Research Training Group foster close cooperation between all three fields. Thus the whole gamut is covered from the application problem through mathematical modeling and the development of efficient algorithms down to the numerical solution.
The research projects of the DFG Research Training Group are interdisciplinary and fall within the following areas:
In the field of Dynamical Processes we concentrate on the analysis of systems which are networked or have complex dynamics. A lot of topics in this field are oriented on applications from the Natural, Engineering or Computer Sciences. Modern techniques of algorithms should be connected with the numerical treatment of dynamical systems to combine numerical analysis and computer science. The aim is to develop new and efficient (numerical) methods for the analysis of the qualitative behavior of dynamic systems.
Project Suggestions:
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In the field of Algorithms and Fundamentals of Complexity Theory we focus on the following topics: complexity theoretic treatment of computation models over the reals, complexity reduction, and algorithms for noisy data. The first topic is related to algorithmic geometry, computer graphics, and complexity theoretic treatment of dynamical systems. The other two topics combine algorithmic fundamental research with applications to e.g. speech recognition.
Project Suggestions:
2.1 | Uniform versus non-uniform computation models over the reals Supervision: Meyer auf der Heide, Bürgisser, von zur Gathen |
2.2 | Computational complexity of topological invariants Supervision: Bürgisser, Meyer auf der Heide |
2.3 | Discrete models for computations over the reals Supervision: Bürgisser, Meyer auf der Heide |
2.4 | Lower bounds for streaming algorithms Supervision: Sohler, Bürgisser |
2.5 | Complexity of lattice problems Supervision: Blömer, von zur Gathen |
2.6 | Lower Bounds for computations over the integers Supervision: Meyer auf der Heide, Bürgisser, Blömer |
2.7 | Dynamical streaming algorithms in geometry Supervision: Sohler, Meyer auf der Heide |
2.8 | Dimension reduction methods to increase classification rates Supervision: Häb-Umbach, von zur Gathen, Meyer auf der Heide |
2.9 | Efficient model reduction for Markov processes Supervision: Blömer, Häb-Umbach, Sohler |
2.10 | Streaming algorithms for matchings in graphs Supervision: Meyer auf der Heide, Sohler |
2.11 | Intelligent sampling to determine the free energy of molecules using coarse decompositions of the phase space Supervision: Dellnitz, Frauenheim |
2.12 | Condition numbers and smoothed analysis Supervision: Bürgisser, Sohler, Monien |
2.13 | Classification of point sets Supervision: von zur Gathen, Meyer auf der Heide, Häb-Umbach |
2.14 | Improvement of speech quality using particle filters Supervision: Häb-Umbach, Blömer |