# Projects

Prof. Dr. Karl-Hermann Neeb

## Current Projects

### Deutsche Forschungsgemeinschaft (DFG)

Nets of standard subspaces on causal symmetric spaces NE 413/10-2

### Alexander-von-Humboldt-Stiftung

Dr. Maria Stella Adamo from the University of Tokyo, Japan, will be conducting research from May 2024 to April 2026 with a Humboldt fellowship for postdoctoral researchers. During her stay at FAU, Dr. Adamo will investigate the properties of mathematical realizations of symmetries in the context of quantum physics. One of these properties is something known as reflection positivity, which demands positivity with respect to a reflection of spacetime. Reflection positivity can be used to investigate quantum models in various mathematical descriptions. Dr. Adamo plans to construct a class of models with several symmetries known as conformal symmetries. She will construct quantum fields by using reflection positivity and the correspondence between classic models and quantum models. Furthermore, Dr. Adamo wants to investigate when deformations of states in quantum field theory (QFT) that describe thermal equilibrium produce thermal states again.

## Past Projects

### Deutsche Forschungsgemeinschaft (DFG)

Ordered dilation spaces and geometry of standard subspaces, NE 413/10-1

Invariant convexity in infinite dimensional Lie algebras, NE 413/9-1

Semibounded unitary representations of infinite dimensional Lie groups, NE 413/7-2, DFG Priority Programme 1388 Representation Theory (Karl-Hermann Neeb, Christoph Zellner)

Semibounded unitary representations of infinite dimensional Lie groups, NE 413/7-1, DFG Priority Programme 1388 Representation Theory (Karl-Hermann Neeb, Christoph Zellner)

### Other

Representation theory of generalized affine Lie algebras, Mercator Visiting Fellowship (Karl-Hermann Neeb, Erhard Neher)

Emerging Field Project Quantum Geometry (Klaus Mecke, Catherine Meusburger, Karl-Hermann Neeb, Thomas Thiemann)