Professorships
Analysis
Analysis (Prof. Dr. Leonhard Frerick: Publications, Prof. Dr. Müller: Publications)
- Function theory: approximation in the complex, linear dynamical systems, Bergman spaces
- Functional analysis: continuation operators, Dirichlet series, non-local operators
Functional Analysis (Prof. Dr. Jochen Wengenroth: Publications)
- Theory and applications of locally convex spaces in distribution theory
- Categorical and homological methods in analysis
Applied Analysis (Prof. Dr. Olaf Post: Publications)
- Spectral and operator theory: convergence of operators in different Hilbert spaces; abstract boundary value problems
- Analysis of energy forms and Laplace operators on metric spaces such as discrete and metric graphs, fractals, and manifolds.
Numerics
Modeling and numerics (Prof. Dr. Nicole Marheineke: Publications)
- Model reduction, asymptotic and hierarchical modeling
- Numerics and optimization with ordinary, partial and stochastic differential equations
Optimization with partial differential equations (Prof. Dr. Schulz: Publications, PD Dr. Stephan Schmidt: Publications)
- Numerical optimization with ordinary and partial differential equations
- Shape optimization, optimal control problems, inverse problems
Optimization
Nonlinear Optimization (Prof. Dr. Martin Schmidt: Publications)
- Mixed integer nonlinear optimization
- Bilevel optimization and equilibrium models
Operations Research (Prof. Dr. Sven de Vries: Publications)
- Discrete, combinatorial and integer optimization
- Game theory: combinatorial auctions and mechanism design
Stochastics
Mathematical stochastics (Prof. Dr. Lutz Mattner: Publications, Prof. Dr. Bero Roos: Publications)
- Statistics: confidence intervals, optimality theory, applications
- Probability theory: approximations, stochastic orders, analytical tools
Stochastics (Prof. Dr. Frank Seifried: Publications)
- Stochastic processes and control theory
- Mathematical Economics and Finance
Current research projects
PHS - Port-Hamilton systems
SFB 1701 (Collaborative Research Centre)
TP B02: Geometric numerical integrators for port-Hamiltonian systems
| Funding agency | Deutsche Forschungsgemeinschaft (DFG) |
Speaker university | Bergische Universität Wuppertal |
Partner universities | TU Berlin, TU Chemnitz, TU Ilmenau, Universität Trier |
| Principal Investigator | Prof. Dr. Nicole Marheineke, Prof. Dr. Michael Günther (Bergische Universität Wuppertal) |
| Time frame | 2025 – 2028 |
Taking into account the effects of ports, dissipation and nonlinear parameterisations, efficient higher-order time integration methods are developed for port-Hamiltonian systems of ordinary differential and differential-algebraic equations. The methods are based on variants of operator splitting, which extend and generalise concepts of commutators, Cayley transformations and multirate approaches. In addition, Galerkin methods and discrete gradient methods specifically tailored to the port-Hamiltonian structure are designed and analysed.
ALOP — Algorithmic Optimization
Research Training Group (RTG 2126)
| Funding agency | German Research Foundation (GRF) |
| Speaker | Prof. Dr. Volker Schulz |
| Principal Investigator | Prof. Dr. Nicole Marheineke, Prof. Dr. Leonhard Frerick, Prof. Dr. Georg Müller-Fürstenberger, Prof. Dr. Ralf Münnich, Prof. Dr. Martin Schmidt, Prof. Dr.Frank Thomas Seifried, Prof. Dr. Sven de Vries, Prof. Dr. Miriam Dür, PD Dr. Jan Pablo Burgard |
| Time frame | 2017 – 2025 |
Mathematical optimization is a discipline of high importance for economy, science, industry, policy support, and the public and private sector. Due to practical demand and the rise of computing capabilities, experts proficient in this field are needed in research and development. This research training group (RTG) therefore focuses on education in the field of algorithmic optimization.
ElAN - Efficient local waste heat utilization in low-temperature networks
Funding agency | BMBF |
| Speaker | Prof. Dr. Nicole Marheineke |
| Principal Investigator | Prof. Dr. Nicole Marheineke |
| Contributors | Andrés Ortegón |
| Time frame | 2022 – 2025 |
The aim of the subproject is the development and analysis of structure-preserving approximations for low-temperature subgrids with fixed flow direction and their application in state estimation for model predictive control. The envisaged data (snapshot)-based reduction under compatibility conditions includes Galerkin projections for spatial discretization and model order reduction as well as complexity reduction for the nonlinearities.
FINE – Forschen durch interaktives Entdecken
| Funding agency | Ministerium für Bildung Rheinland-Pfalz (MB), Ministerium für Familie, Frauen, Kultur und Integration Rheinland-Pfalz (MFFKI) |
| Speaker | Dr. Bernd Perscheid |
| Principal Investigator | Dr. Bernd Perscheid, Bianca Schröder |
| Time frame | 2025 |
Educational project for elementary school children in full-day programs to promote mathematical skills.
Ada-Lovelace-Project
Ada-Lovelace-Project
| Funding agency | European Social Fund Plus, Ministry of Science and Health (MWG), Ministry of Family, Women, Culture and Integration (MFFKI) |
| Sprecher | Prof. Dr. Leonhard Frerick |
| Principal Investigator | Bianca Schröder |
| Time frame | since 1998 |
Rhineland-Palatinate Competence Center for Women in STEM