Department of Mathematics

# Areas of Research

The six institutes in the department cover many important research areas in mathematics.

The Department of Mathematics conducts research in many important and modern fields of mathematics. On the one hand, strong fundamental research and the interplay between mathematical fields play a key role. On the other hand, research topics are inspired by interdisciplinary questions in natural, engineering, life and economic sciences, leading to the development of new mathematical methods and foundations.

Members of the Department of Mathematics participate in the **Cluster of Excellence SimTech** and in various **Collaborative Reseach Centers and Research Training Groups**. They maintain strong international and national collaborations, and sustain several large** software projects**.

## Research Areas

Prof. Dr. M. Geck |
Representation theory, Computer algebra |

Prof. Dr. A. Henke |
Representation theory of groups and algebras, Combinatorial representation theory, Algebraic combinatorics |

Prof. Dr. S. König |
Algebra, Representation theory, Homological and categorical structures |

Prof. Dr. M. Griesemer |
Dynamics and spectral theory of many-particle quantum systems, Variational methods in quantum mechanics |

Prof. TeknD T. Weidl |
Spectral theory, Mathematical physics |

Apl. Prof. Dr. J. Wirth |
Analysis of partial differential equations, Operator theory, Harmonic analysis in R^{n} and on Lie groups |

Apl.Prof. Dr. W.-P. Düll |
Nonlinear partial differential equations, Mathematical fluid mechanics, Justification of approximation equations, Multi-scale methods in mathematical modelling |

Prof. Dr. J. Pöschel |
Dynamical systems, Stability of Hamiltonian systems, KAM-theory |

Prof. Dr. C. Scherer |
Systems theory and optimisation, Analysis of uncertain dynamical systems, Robust controller synthesis |

Prof. Dr. G. Schneider |
Nonlinear partial differential equations, Diffusive and dispersive dynamics, Multi-scale problems in mathematical modelling |

Priv.-Doz. Dr. A. Degeratu |
Differential geometry, Complex geometry, Partial differential equations, Gauge theory, Mathematical physics, Mathematical biology |

Prof. Dr. M. Eisermann |
Geometric topology, Low-dimensional manifolds, Group theory, Algorithms and computer algebra |

Prof. Dr. U. R. Freiberg |
Analysis and stochastics on fractals, Random fractals, Krein-Feller-theory, Quantum graphs, Graphs and networks |

Priv.-Doz. Dr. M. Hamilton |
4-dimensional manifolds, Geometric topology, Mathematical and theoretical physics |

Apl. Prof. Dr. A. Kollross |
Lie group actions, Riemannian homogeneous and symmetric spaces |

Prof. Dr. U. Semmelmann |
Spin geometry and Dirac operators, Geometric differential equations, Holonomy theory and special geometric structures |

Prof. Dr. F. Witt |
Differential geometry, Complex geometry |

Priv.-Doz. Dr. A. Degeratu |
Differential geometry, Complex geometry, Partial differential equations, Gauge theory, Mathematical physics, Mathematical biology |

Apl.Prof. Dr. W.-P. Düll |
Nonlinear partial differential equations, Mathematical fluid mechanics, Justification of approximation equations, Multi-scale methods in mathematical modelling |

Prof. Dr. M. Griesemer |
Dynamics and spectral theory of many-particle quantum systems, Variational methods in quantum mechanics |

Priv.-Doz. Dr. M. Hamilton |
4-dimensional manifolds, Geometric topology, Mathematical and theoretical physics |

Priv.-Doz. Dr. P. Lesky |
Partial differential equations, Spectral theory for self-adjoint operators, Energy estimates for solutions of nonlinear wave equations |

Prof. Dr. J. Pöschel |
Dynamical systems, Mathematical and theoretical physics, KAM-theory |

Prof. TeknD T. Weidl |
Spectral theory, Mathematical physics |

Prof. Dr. F. Witt |
Mathematical and theoretical physics |

Apl. Prof. Dr. W.-P. Düll |
Nonlinear partial differential equations, Mathematical fluid mechanics, Justification of approximation equations, Multi-scale methods in mathematical modeling |

Priv.-Doz. Dr. J. Giesselmann |
Hyperbolic conservation laws, Compressible multi-phase flow |

Prof. Dr. B. Haasdonk |
Model reduction and data-based modelling, Numerical simulation, Machine learning |

Priv.-Doz. Dr. I. Rybak |
Flows in porous media, numerical methods for multi-scale problems |

Prof. Dr. G. Schneider |
Nonlinear partial differential equations, Diffusive and dispersive dynamics, Multi-scale problems in mathematical modelling |

Prof. Dr. A. Barth |
Stochastic partial differential equations, Uncertainty quantification, Stochastic analysis |

Prof. Dr. D. Göddeke |
High performance computing, GPU computing, Applications in optimisation, geo- and life sciences |

Prof. Dr. B. Haasdonk |
Model reduction and data-based modelling, Numerical simulation, Machine learning |

Prof. Dr. C. Rohde |
Modelling, analysis, simulation with nonlinear partial differential equations, Mathematical fluid mechanics / CFD |

Priv.-Doz. Dr. I. Rybak |
Flows in porous media, Numerical methods for multi-scale problems |

Prof. Dr. C. Scherer |
Systems theory and optimisation, Analysis of uncertain dynamical systems, Robust controller synthesis |

Priv.-Doz. Dr. A. Degeratu |
Differential geometry, Complex geometry, Partial differential equations, Gauge theory, Mathematical physics, Mathematical biology |

Apl. Prof. Dr. W.-P. Düll |
Nionlinear partial differential equations, Mathematical fluid mechanics, Justification of approximation equations, Multi-scale methods in mathematical modelling |

Priv.-Doz. Dr. J. Giesselmann |
Hyperbolic conservation laws, Compressible multi-phase flow |

Prof. Dr. C. Rohde |
Modelling, analysis, numerics with nonlinear partial differential equations, Mathematical fluid mechanics / CFD |

Prof. Dr. G. Schneider |
Nonlinear partial differential equations, Diffusive and dispersive dynamics, Multi-scale problems in mathematical modelling |

Apl. Prof. Dr. J. Wirth |
Analysis of partial differential equations, Operator theory, Harmonic analysis in R^{n} and on Lie groups |

Prof. Dr. A. Barth |
Stochastic partial differential equations, Uncertainty quantification, Stochastic analysis |

Priv.-Doz. Dr. J. Dippon |
Stochastic analysis, Stochastic models in biology and medicine, Mathematical finance |

Prof. Dr. U. R. Freiberg |
Analysis and stochastics on fractals, Random fractals, Krein-Feller-theory, Quantum graphs, Graphs and networks |

Prof. Dr. C. Hesse |
Nonparametric theory of estimation, especially deconvolution, Statistical analysis of voting systems, Differential equations with random initial conditions |

Prof. Dr. I. Steinwart |
Statistical learning theory and machine learning, Cluster analysis |

Prof. Dr. M. Eisermann |
Geometric topology, in particular low-dimensional manifolds, Group theory, Algorithms and computer algebra |

Prof. Dr. D. Göddeke |
High performance computing, GPU computing, Applications in optimisation, geo- and life sciences |

Prof. Dr. I. Steinwart |
Efficient implementations of learning algorithms, Applications for learning algorithms |