Research Overview
The research themes of the institute are listed according to their main characteristic (mathematical research topics and applications).
Mathematical Research Topics
- Analysis of Partial Differential Equations and Evolutionary Equations
- Analysis of ordinary and partial stochastic differential equations
- Development and analysis of financial models
- Direct and inverse problems for the Maxwell equations
- Direct and inverse problems in thermomechanics
- Free boundary problems for partial differential equations
- Functional analysis and operator theory
- Hysteresis operators and rate-independent systems
- Interacting stochastic particle systems
- Large deviations
- Methods for optimal stopping and control
- Modeling, analysis and numerics of phase field models
- Multi-scale modeling, asymptotic analysis, and hybrid models
- Numerical Methods for PDEs with Stochastic Data
- Numerical methods for problems from fluid dynamics
- Optimal Transport: Statistics, Numerics, and Partial Differential Equations
- Optimal control of partial differential equations and nonlinear optimization
- Random geometric systems
- Statistical Inference
- Statistical inverse problems
- Stochastic Optimization
- Systems of partial differential equations: modeling, numerical analysis and simulation
- Theory of dynamical systems
- Variational methods
Applications
- Applications in diffractive optics
- Calibration and risk assesment of stock and interest rate models
- Coagulation
- Diffusion models in statistical physics
- Dynamics of semiconductor lasers
- Electronic materials
- Mathematical Models and Methods for Lithium-ion Batteries
- Medical imaging and neuroscientific applications
- Mobile Communication Networks
- Modeling and simulation of semiconductor structures
- Modeling of thin films and nano structures on substrates
- Modeling, Simulation and Optimization for Biomedical Applications
- Nonlinear material models, multifunctional materials and hysteresis in continuum mechanics.
- Optical pulses in nonlinear media
- Optimization Problems in Energy Management
- Particle-based modeling in the Sciences
- Phase field models for complex materials and interfaces
- Quantum models for semiconductors
- Simulation and optimization of industrial processes
- Thermodynamic models for electrochemical systems
- Valuation of complex structured instruments in financial and energy markets
Infrastructure Themes
Archive
Topics that are not treated at the moment but where the institute has expertise in:Mathematical research topics
- Algorithms for the generation of 3D boundary conforming Delaunay meshes
- Magnetohydrodynamics
- Nonlinear kinetic equations
- Plates, Beams, Shells and Arches
- Spectral theory of random operators
Application topics
- Crystal growth under the influence of electromagnetic fields
- Modeling and simulation of photoresists
- Numerical methods for the simulation of population balance systems
- Photovoltaics
- Production of solar silicon
- Static and dynamic simulation in process engineering
- Stochastic Biological Evolution
- Unwanted precipitates during heat treatment of GaAs single crystals
- Volatility estimation and risk management