# Research Area C:

# Mathematics of quantum physics

Historically there has always been a strong and fruitful interplay between quantum physics and mathematics. E.g. quantum mechanics and the spectral theory of operators in Hilbert space as well as the foundations of operator algebras were developed essentially in parallel. Modern fields of mathematics such as quantum theory, mirror symmetry or topological field theory emerged basically from the still unsolved problem of finding a rigorous theory of the Feynman path integral. The scientists of this research area strive to contribute to these highly attractive areas of mathematics. In particular, they are concerned with:

- Mirror symmetry,
- Topological and integrable quantum systems,
- Operator algebras,
- Quantum theory,
- Field theory.