Indextheorie angewandt auf quantenmechanische und klassische Systeme

Drittmittelfinanzierte Einzelförderung

Details zum Projekt

Prof. Dr. Hermann Schulz-Baldes

Beteiligte FAU-Organisationseinheiten:
Professur für Mathematik (Mathematische Physik)

Mittelgeber: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Projektstart: 01.01.2016
Projektende: 31.12.2018
Laufzeitverlängerung bis: 01.10.2019

Abstract (fachliche Beschreibung):

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.

Zuletzt aktualisiert 2019-21-02 um 08:58