Research Areas
The behavior of many mathematical and physical models is determined by a complex interplay between multiple length, time and energy scales. In our research we are interested in mathematical models, where details on small scales may lead to the emergence of new, effective properties on larger scales. Understanding this connections and predicting large-scale effective properties by means of mathematical analysis is one of our goals.
In our works we mainly focus on PDEs and variational models that feature multiple length scales, randomness, and nonlinearities. A leitmotif is homogenization theory, which is about rigorously passing from models with one or more small scales to a macroscopic, effective description. The problems we are interested in typically live on the interface between applied analysis, continuum mechanics, probability theory, and sometimes are related to mathematical physics.
Our main research areas are:
- Stochastic homogenization and in particular quantitative stochastic homogenization
- Multiscale Problems in Nonlinear Elasticity
- Discrete-to-Continuum Analysis
For our funded projects see here.