Research Area

Mathematical Sciences

The title: Mathematical sciences of this Top-Level Research Area 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, active research concentrates on structural questions arising directly from physics and increasingly also from biological problems. This field of research is also one of major interest to the institute of computer science, which has applied computer sciences as one of three research fields, which has an emphasis on applications in the Life Sciences. The joint project is driven by the insight, that problems 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 areas within this Top-Level Research Area are

• Quantumstructures
• Multiscale problems in analysis and stochastics
• Complex systems: mathematical methods, computational tools, biological models

• Riemannian Geometry, dynamical systems, complex analysis
• Algebraic Geometry, 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