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Research Fields

Research at the Department of Mathematics covers many areas of mathematics. On the one hand inner-mathematical questions play a key role. It is particularly fruitful to study the relationship of various mathematical fields among themselves and to apply methods of one field to another. Furthermore, many interesting problems are motivated by problems in the natural and engineering sciences and economics. Current topics include the following fields:

Institute of Algebra and Number Theory

Prof. Dr. S. König Algebra, representation theory, homological and categorical structures
Prof. Dr. M. Geck Representation theory, groups of Lie type, computer algebra
Prof. Dr. A. Henke Representation theory of groups and algebras, combinatorial representation theory, algebraic combinatorics
Prof. Dr. Wolfgang Rump Categorical representation theory, quantum theory and I-groups, triangulated categories

Institute of Analysis, Dynamics and Modeling

Prof. TeknD T. Weidl Spectral theory, mathematical physics
Prof. Dr. G. Schneider
Nonlinear partial differential equations, justification of amplitude equations, diffusive and dispersive dynamics
Prof. Dr. M. Griesemer Dynamics of quantum systems, justification of amplitude equations, diffusive and dispersive dynamics
Prof. Dr. J. Pöschel Dynamical systems, stability theory of Hamiltonian systems, KAM theory, astropaleobotany
Priv.-Doz. P. Lesky Partial differential equations, spectral theory for self-adjoint operators,
resonance and decay occuring by solutions of wave-equations in unbounded domains, energy estimates for solutions of nonlinear wave equations
Priv.-Doz. J. Wirth Analysis of partial differential equations, operator theory, harmonic analysis in Rn and on Lie groups
Priv.-Doz. W.-P. Düll Nonlinear partial differential equations, mathematical fluid mechanics, justification of approximation equations

Institute of Applied Analysis and Numerical Simulation

Prof. Dr. C. Rohde Nonlinear partial differential equations, modeling, analysis, numerics, mathematical fluid mechanics/CFD
Prof. Dr. K.G. Siebert Numerical analysis and scientific computing, partial differential equations
Prof. Dr. D. Göddeke High-performance computing, parallel numerics, fast solvers
Prof. Dr. B. Haasdonk Model reduction, numerical analysis, scientific computing
Jun.-Prof. Dr. A. Barth Solution theory and numerical analysis for stochastic partial differential equations, stochastic analysis
Priv.-Doz. Dr. I. Rybak Flows in porous media, averaging theories, numerical methods for multi-scale problems

Institute of Geometry und Topology

Prof. Dr. U. Semmelmann Spin geometry and Dirac operators, geometric differential equations, Holonomy theory and special geometric structures
Prof. Dr. F. Witt Gauge theory, special holonomy, complex geometry
Prof. Dr. M. Eisermann Geometric topology, especially low-dimensional manifolds; knot theory and Zopf groups, their representations and invariants; group theory, algorithms and computer algebra
Prof. Dr. W. Kimmerle Group and representation rings, crystallography, integral group rings and lattices, representation theory of groups and group theory automorphisms of simplicial complexes
Priv.-Doz. Dr. M. Hamilton 4-dimensional manifolds, geometric topology, mathematical and theoretical physics
Priv.-Doz. Dr. A. Kollross Lie group actions, Riemannian homogeneous and symmetric spaces

Institute of Mathematical Methods in Engineering, Numerical Analysis and Geometric Modeling

Prof. Dr. C. Scherer Optimization in control, analysis of uncertain dynamical systems, robust controller design
Prof. Dr. K. Höllig Finite elements, approximation and modeling, B-splines
Priv.-Doz. Dr. J. Giesselmann Hyperbolic conservation equations, compressible multiphase flows, discontinuous Galerkin methods

 

Institute of Stochastics and Applications

Prof. Dr. I. Steinwart Statistical learning theory and machine learning, theory and implementation of kernel-based learning methods, cluster analysis
Prof. Dr. C. Hesse Nonparametric estimation theory, especially deconvolution; statistical analysis of voting systems; differential equations with noisy data; stochastic dynamics of many-body systems
Prof. Dr. U. R. Freiberg Stochastic processes and fractal path properties, potential theory on fractals, dimension theory of random fractals
Priv.-Doz. Dr. J. Dippon Stochastic analysis, stochastic models in life sciences, mathematical finance