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 at the intersection of analysis, algebra and combinatorics. Amongst others, I am primarily dealing with methods from functional analysis, links to free probability theory and symmetry structures of geometries within any framework, in particular a noncommutative one. I am mainly dealing with noncommutative algebras arising in the context of operators on Hilbert spaces, matrices in linear algebra or observables in quantum physics. My central objects are compact quantum groups and I am investigating them 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
  • Combinatorics: partitions of sets, finite graphs, counting problems
  • Algebra: Hopf algebras, automorphisms of graphs, computer algebra
  • 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
  • Mathematical physics: quantum mechanics (by von Neumann), notions of symmetry
  • Stochastical methods: distributional symmetries, free probability, Levy processes

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 is: I.13 - Computational classification of orthogonal quantum groups.

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!

Publications

Preprints

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  • Mang, Alexander; Weber, M.
    Categories of two-colored pair partitions, Part II: Categories indexed by semigroups
    arXiv:1901.03266 [math.CO, math.QA], 37 pages (2019).

  • Gromada, Daniel; Weber, M.
    Intertwiner spaces of quantum group subrepresentations
    arXiv:1811.02821 [math.QA, math.OA], 38 pages (2018).

  • Weber, M.
    Partition C*-algebras
    arXiv:1710.06199 [math.OA, math.CO, math.QA], 19 pages + 11 pages of appendix and references (2017).

  • Weber, M.
    Partition C*-algebras II - links to compact matrix quantum groups
    arXiv:1710.08662 [math.OA, math.CO, math.QA], 27 pages (2017).

  • Cébron, Guillaume; Weber, M.
    Quantum groups based on spatial partitions
    arXiv:1609.02321 [math.QA, math.OA], 32 pages (2016).

  • Speicher, Roland; Weber, M.
    Quantum groups with partial commutation relations
    arXiv:1603.09192 [math.QA, math.OA], 44 pages (2016).


Monographs

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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

  • Weber, M.
    Basics in free probability, 6 pages
    in Free probability and operator algebras, ed. by Dan-V. Voiculescu, N. Stammeier, M. Weber, EMS, 2016.

  • Weber, M.
    Easy quantum groups, 23 pages
    in Free probability and operator algebras, ed. by Dan-V. Voiculescu, N. Stammeier, M. Weber, EMS, 2016.


in peer reviewed journals

Show abstracts


Further publications



Further publications by students under my supervision






updated: 21 January 2019   Moritz Weber Impressum