Prof. Dr. Moritz Weber

Research interest
List of publications
    - in peer reviewed journals
    - monographs
    - preprints
    - further publications
Further publications by students under my supervision
My articles on Google Scholar
My articles on Math Sci Net
My articles on arXiv
PI in the SFB-TRR 195
Editor of Analysis Mathematica

Research interest

My research is on compact quantum groups. I am working at the intersection of analysis, algebra and combinatorics, with links to free probability. Amongst others, I am primarily interested in symmetry structures within any framework, in particular a noncommutative one, i.e. structures involving noncommutative algebras arising in the context of operators on Hilbert spaces, matrices in linear algebra or observables in quantum physics, just to name a few. I am investigating compact quantum groups from different perspectives, using various methods interfering with many other areas of mathematics such as:
  • Functional analysis: (universal) C*-algebras, von Neumann algebras, K-Theory
  • Algebra: Hopf algebras, automorphisms of graphs, computer algebra
  • Combinatorics: partitions of sets, finite graphs, counting problems
  • Topology, cohomology: noncommutative topology (C*-algebras), K-Theory, (Hochschild) cohomology
  • Quantum symmetries: "easy" quantum groups, noncommutative harmonic analysis, quantum automorphisms of graphs
  • Geometry: noncommutative geometry, notions of symmetry, deformation/quantization
  • Tensor categories: representation theory of quantum groups, Schur-Weyl results
  • Quantum information theory: graph isomorphism games, construction of highly entangled quantum states
  • Stochastical methods: distributional symmetries, free probability, Lévy processes
My main expertise is around "easy" quantum groups and the strategy to express analytic, algebraic or representation theoretical properties by purely combinatorial means.

What actually is Quantum Symmetry (Oberwolfach Snapshot)?

Moritz Weber, Stefan Jung, Laura Maaßen, Daniel Gromada, Simon Schmidt, Alexander Mang (May 2019)
PhD students

Member (PI) of the SFB-TRR 195

Since 1 January 2017, I am one of the PI's of the SFB-TRR 195 Symbolic Tools in Mathematics and their Applications (RWTH Aachen, TU Kaiserslautern, Saarland University, and others), funded by the DFG (German Research Foundation).
My project in the first phase (2017-2020) was: I.13 - Computational classification of orthogonal quantum groups.
My project in the second phase (2021-2024) is: A25 - Quantum symmetries and quantum isomorphisms of graphs

Editor of Analysis Mathematica

Since January 2019, I am an editor of Analysis Mathematica for the area functional analysis, operator algebras and quantum groups. Submissions welcome!

Alternative journals with editors coming from operator algebras may be found on a list by Hannes Thiel.



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Weber, M.
Basiswissen Mathematik auf Arabisch und Deutsch
Springer Spektrum, 2018
168 pages

Voiculescu, Dan-Virgil; Stammeier, Nicolai; Weber, M. (eds)
Free probability and operator algebras
Münster Lecture Notes in Mathematics
European Mathematical Society (EMS)
132 pages
Zürich, 2016

Chapters in monographs

in peer reviewed journals

Show abstracts

Further publications

Further publications by students under my supervision

updated: 17 November 2020   Moritz Weber Impressum