Philosophy of the Research Area
In this research area the term "Mathematical Sciences" is understood in a broad sense: mathematics, theoretical physics and large parts of computer science. The unifying theme for all researchers in this research area is mathematics.
The Institute of Mathematics, founded 125 years ago by Felix Klein, and the Institute for Theoretical Physics have a long history of collaboration. Together with the Max Planck Institute for Mathematics in the Sciences and the Institute of Computer Science, they concentrate their active research on structural questions arising directly from physics and increasingly also from biological problems. The issue of applications in the Life Sciences is one of the main research areas in the department of applied computer science.
The joint project is driven by the insight that the problems in question cannot successfully be solved by already existing mathematical tools but need new mathematical methods. In this way, as in the past, mathematics is profiting from its applications.
Three major research subjects within this Top-Level Research Area are:
- Quantum structures
- Multiscale problems in analysis and stochastic
- Complex systems: mathematical methods, computational tools, biological models
These are linked to fundamental questions of modern science: Unification of field theories, loss of predictability and the nature of probability in large scale systems, self-organisation of living matter. There are further projects dealing also with applications beyond the realm of natural sciences. Particular fields of competence of the scientists involved in this Top-Level Research Area are:
- Riemannian geometry, dynamical systems, complex analysis
- Algebraic topology, symplectic geometry
- Geometric and functional analytic methods in mathematical physics
- Quantum field theory, particle theory
- Theory of gravitation
- Partial differential equations, calculus of variations
- Stochastic processes, stochastic analysis and mathematics of finance
- Statistical physics, condensed matter physics
- Discrete mathematics, applied computer science, bioinformatics, theoretical computer sciences
- Mathematical biology