Dr. Malte Gerhold
Junior Fellow, October 2025 to September 2026
Saarland University
- Postdoctoral fellow at Technion – Israel Institute of Technology, Haifa, as ERCIM Fellow at the Norwegian University of Science and Technology (NTNU), Trondheim, and at Saarland University (UdS), Saarbrücken
- Studied mathematics and conducted research at the University of Greifswald (2004–2015; doctorate), followed by six years as a research assistant
Fellow project: „A Metric Approach to the Rigidity of Operator Systems via Dilations“
This research project lies in the field of operator theory, with connections to noncommutative geometry and potentially to mathematical physics.
The main goal of the project is to define a rigidity property for operator systems based on the concept of dilation distance, which we developed together with Shalit, and to relate it to other notions of rigidity, in particular Arveson's hyperrigidity and Thompson’s approximate unique extension property. It is expected that hyperrigidity will turn out to be the strongest among the considered notions of rigidity. The central question is whether any of the remaining properties implies the other.
In addition, the scope of the dilation distance shall be extended beyond unitarily generated operator systems to broader classes, especially those closely related to compact quantum groups. This is tied to two hopes, which cannot be assessed conclusively at this point. On the one hand, similar to the noncommutative tori, one may hope to find continuity results for certain bundles of compact quantum groups (in particular the free unitary and free orthogonal quantum groups). On the other hand, notions of continuity for stochastic processes on quantum groups developed via the dilation distance may offer new perspectives on the question whether Gaussian processes can be characterised via a suitable continuity condition (classically, they are precisely the path-continuous ones, but in the noncommutative case, there are no paths).