Applied index theory for quantum and classical systems

• Applicant: Professor Dr. Hermann Schulz-Baldes
• Subject Area: Mathematics ; Theoretical Condensed Matter Physics
• Term: from 2015 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 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 Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Dr. Terry Loring