Analysis constitutes (together with numerical simulation) the methodical basis of most of applied mathematics. Its ideas and methods play an important role in a wide spectrum of fields, ranging all the way from rather applied corners of science and engineering to pretty theoretical branches of mathematics like geometry and topology.
The research of our group focuses on the analysis of concrete mathematical models from science and engineering, typically from electronic structure, molecular mechanics/dynamics, continuum mechanics. Usually we are interested in
- understanding emergent phenomena and collective effects which are not obvious from the simple rules specified by the model and appear on much larger length- or timescales,
- understanding connections between models, e.g. rigorously reducing models to simpler ones which retain key effects or may even capture them more clearly.
A hallmark of our group is that in our projects we don't just confine ourselves to the required foundational analytical work, but we also carry out the translation work mathematics ↔ underlying area of science, in close collaboration with physicists, chemists, biologists, material scientists. Our mathematical core expertise is in calculus of variations, functional analysis, PDEs, multiscale methods; beyond that, numerical extraction of predictions and validation against experimental data also play an important role.
A key objective of the Analysis Chair is the communication of interdisciplinary connections between mathematics and the sciences in our teaching, for instance within the framework of the studium naturale.