Indextheorie angewandt auf quantenmechanische und klassische Systeme

• Antragsteller: Professor Dr. Hermann Schulz-Baldes
• Fachliche Zuordnung: Mathematik ; Theoretische Physik der kondensierten Materie
• Förderung: Förderung von 2015 bis 2023
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 281672735

The first goal of index theory is to relate topological invariants to indices of Fredholm operators. The most famous result in this direction is the Atiyah-Singer index theorem, but there exist far reaching non-commutative generalizations. While there is a general theory, such index theorems have to be established case by case in applications. The second goal of index theory is to connect invariants and indices of problems related via exact sequences. For example, this allows to read off the topology of boundary states or point defects from bulk invariants. The proposal aims to implement this program in situations which have not been tackled before like interacting spin systems, photonic crystals and lattices of classical springs, and also to further develop the index approach to scattering systems and topological materials.

• DFG-Verfahren: Sachbeihilfen
• Internationaler Bezug: USA
• Kooperationspartner: Professor Dr. Terry Loring