Possible topics for a Masters thesis

1. Elaboration of the abstract quantum space underlying  simple examples of quantum geometries, such as the fuzzy disk or the
   squashed fuzzy sphere.
   Required background: solid understanding of quantum mechanics, good background in differential geometry (manifolds),
   computing skills  (Mathematica)
   
   project-related literature:
   
   H.CSteinacker,  "Quantum (Matrix) Geometry and Quasi-Coherent States", https://arxiv.org/abs/2009.03400
   
   

2. Developing a software package to "measure" quantum geometries, building on or improving upon
    L. Schneiderbauer, Bprobe: a wolfram mathematica package, 2016, doi:10.5281/zenodo.45045.    (= a previous Master's project!)
   
   using the new insights obtained in
   
   H.C.Steinacker,  "Quantum (Matrix) Geometry and Quasi-Coherent States", https://arxiv.org/abs/2009.03400
   
   
3. Refinement of the string state technology developed in [1], in particular elaborating exact representations and estimates for the propagator in this representation.
   This may be appealing for a ambitious mathematically-minded student.
   Required background: strong background in general theoretical and mathematical physics, some field theory.
   
   project-related literature:
   [1] H. C. Steinacker, ``String states, loops and effective actions in noncommutative field theory and matrix models,'' Nucl. Phys. B 910, 346 (2016) [arXiv:1606.00646]