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.

Publications

Preprints

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• Brannan, Michael; Eifler, Kari; Voigt, Christian; Weber, M.
  Quantum Cuntz-Krieger algebras
  arXiv:2009.09466 [math.OA, math.QA], 40 pages (2020).
  

• Schmidt, Simon; Vogeli, Chase; Weber, M.
  Uniformly vertex-transitive graphs
  arXiv:1912.00060 [math.CO], 17 pages (2019).
  

• Eder, Christian; Levandovskyy, Viktor; Schanz, Julien; Schmidt, Simon; Steenpass, Andreas; Weber, M.
  Existence of quantum symmetries for graphs on up to seven vertices: a computer based approach
  arXiv:1906.12097 [math.QA, math.CO], 15 pages + appendix (2019).
  

• 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).
  

Monographs

Show abstracts

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

• Gromada, Daniel; Weber, M.
  Generating linear categories of partitions
  to appear in Kyoto Journal of Mathematics, 2021
  arXiv:1904.00166 [math.CT, math.QA], 19 pages (2019).
  

• Nechita, Ion; Schmidt, Simon; Weber, M.
  Sinkhorn algorithm for quantum permutation groups
  to appear in Experimental Mathematics, 2021
  arXiv:1911.04912 [math.QA], 16 pages (2019).
  

• Mang, Alexander; Weber, M.
  Non-Hyperoctahedral Categories of Two-Colored Partitions, Part II: All Possible Parameter Values
  to appear in Applied Categorial Structures, 2021
  arXiv:2003.00569 [math.CO, math.QA], 34 pages (2020).
  

• Mang, Alexander; Weber, M.
  Non-hyperoctahedral categories of two-colored partitions, Part I: New categories
  to appear in Journal of Algebraic Combinatorics, 2021
  arXiv:1907.11417 [math.CO, math.QA], 30 pages (2019).
  

• Mang, Alexander; Weber, M.
  Categories of two-colored pair partitions, Part II: Categories indexed by semigroups
  Journal of Combinatorial Theory, Series A, Vol. 180, 105509, 43 pp., 2021
  See also arXiv:1901.03266 [math.CO, math.QA], 37 pages (2019).
  

• Gromada, Daniel; Weber, M.
  New products and Z₂-extensions of compact matrix quantum groups
  to appear in Annales de l'Institut Fourier
  arXiv:1907.08462 [math.QA, math.OA], 39 pages (2019).
  

• Junk, Luca; Schmidt, Simon; Weber, M.
  Almost all trees have quantum symmetry
  Archiv der Mathematik, Vol. 115, 267-278, 2020.
  arXiv:1911.02952 [math.CO, math.QA], 11 pages (2019).
  

• Jung, Stefan; Weber, M.
  Models of quantum permutations. With an appendix by Alexandru Chirvasitu and Pawel Joziak
  Journal of Functional Analysis, Vol. 279, Issue 2, 1 August 2020, 108516
  See also: arXiv:1906.10409 [math.OA, math.QA], 24 pages.
  

• Gromada, Daniel; Weber, M.
  Intertwiner spaces of quantum group subrepresentations
  Communications in Mathematical Physics, Vol. 376, 81-115, 2020.
  See also: arXiv:1811.02821 [math.QA, math.OA], 38 pages.
  

• Speicher, Roland; Weber, M.
  Quantum groups with partial commutation relations
  Indiana University Mathematics Journal, Vol. 68, 1849-1883, 2019.
  See also: arXiv:1603.09192 [math.QA, math.OA], 44 pages (2016).
  

• Mang, Alexander; Weber, M.
  Categories of two-colored pair partitions, Part I: Categories indexed by cyclic groups
  The Ramanujan Journal, Vol. 53, 181-208, 2020.
  arXiv:1809.06948 [math.CO, math.QA], 25 pages (2018).
  

• Weber, M.; Zhao, Mang
  Factorization of Frieze patterns
  Revista de la Union Matematica Argentina, Vol. 60 (2), 407-415, 2019
  See also: arXiv:1809.00274 [math.CO], 9 pages.
  

• Jung, Stefan; Weber, M.
  Partition quantum spaces
  Journal of Noncommutative Geometry, Vol. 14, Issue 3, 821-85, 2020
  arXiv:1801.06376 [math.OA, math.FA], 35 pages (2018).
  

• Schmidt, Simon; Weber, M.
  Quantum symmetries of graph C*-algebras
  Canadian Mathematical Bulletin 61, 848-864, 2018
  See also: arXiv:1706.08833 [math.OA, math.FA], 18 pages.
  

• Tarrago, Pierre; Weber, M.
  The classification of tensor categories of two-colored noncrossing partitions
  Journal of Combinatorial Theory, Series A, Vol. 154, Feb 2018, 464-506
  See also: arXiv:1509.00988 [math.CO, math. QA], 40 pages.
  

• Weber, M.
  Introduction to compact (matrix) quantum groups and Banica-Speicher (easy) quantum groups
  Notes of a lecture series at IMSc Chennai, India, 2015
  Indian Academy of Sciences. Proceedings. Mathematical Sciences, Vol. 127, Issue 5, pp 881-933, Nov 2017.
  

• Mai, Tobias; Speicher, Roland; Weber, M.
  Absence of algebraic relations and of zero divisors under the assumption of finite full
               non-microstates free entropy dimension
  Advances in Mathematics, Vol. 304, 2 January 2017, pages 1080-1107.
  See also: arXiv:1502.06357 [math.OA], 25 pages.
  (we extended the former version arXiv:1407.5715 substantially)

• Tarrago, Pierre; Weber, M.
  Unitary easy quantum groups: the free case and the group case
  International Mathematics Research Notes, 18, 1 Sept 2017, 5710-5750.
  See also: arXiv:1512.00195 [math. QA, math.OA], 39 pages.
  

• Gabriel, Olivier; Weber, M.
  Fixed point algebras for easy quantum groups
  SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 12 (2016), 097, 21 pages.
  See also: arXiv:1606.00569 [math.OA, math.KT], 21 pages.
  

• Freslon, Amaury; Weber, M.
  On bi-free De Finetti theorems
  Annales Mathématiques Blaise Pascal, 23(1), 21-51, 2016.
  See also: arXiv:1501.05124 [math.PR, math.OA, math.QA], 16 pages.
  

• Raum, Sven; Weber, M.
  The full classification of orthogonal easy quantum groups
  Communications in Mathematical Physics, 341(3), 751-779, Feb 2016.
  See also: arXiv:1312.3857 [math.QA], 38 pages.
  

• Raum, Sven; Weber, M.
  Easy quantum groups and quantum subgroups of a semi-direct product quantum group
  Journal of Noncommutative Geometry, Vol. 9(4), 1261-1293, 2015
  See also: arXiv:1311.7630 [math.QA], 26 pages.
  

• Freslon, Amaury; Weber, M.
  On the representation theory of partition (easy) quantum groups
  Journal für die reine und angewandte Mathematik [Crelle's Journal], Vol. 2016, Issue 720 (Nov 2016), 2016.
  See also: arXiv:1308.6390 [math.QA], 42 pages.
  

• Raum, Sven; Weber, M.
  The combinatorics of an algebraic class of easy quantum groups
  Infinite Dimensional Analysis, Quantum Probability and related topics Vol 17, No. 3, 2014.
  See also: arXiv:1312.1497 [math.QA], 16 pages.
  

• Weber, M.
  On the classification of easy quantum groups
  Advances in Mathematics, Volume 245, 1 October 2013, pages 500-533.
  See also: arXiv:1201.4723 [math.OA], 39 pages.

• Weber, M.
  On C*-Algebras Generated by Isometries with Twisted Commutation Relations
  Journal of Functional Analysis, Volume 264, Issue 8, pages 1975-2004, 2013.
  See also: arXiv:1207.3038 [math.OA], 35 pages.

Further publications

• Weber, M.
  Berichte über Arbeitsgruppen. SFB/TRR 195 Symbolic Tools in Mathematics and their Application (Part 4/5).
  Random matrices, free probability theory and compact quantum groups
  Computeralgebra-Rundbrief Nr. 65, Oktober 2019.

• Weber, M.
  Quantum symmetry
  Snapshots of modern mathematics from Oberwolfach, 2020.
  

• Weber, M.
  Auffrischungskurs Mathematik für Geflüchtete - ein best practice example
  in Kergel, D., Heidkamp, B. (Hrsg.) (2018). Praxishandbuch habitus- und diversitätssensible Hochschullehre,
  VS Springer, 2019.
  arising from the preparatory math courses for refugees for studies in MINT-subjects

Further publications by students under my supervision

• Schmidt, Simon
  Quantum symmetry vs nonlocal symmetry
  arXiv:2012.13328 [math.QA, math.CO, quant-ph], 44 pages (2020).

• Gromada, Daniel
  Group-theoretical graph categories
  arXiv:2009.06998 [math.QA, math.CO], 30 pages (2020).

• Gromada, Daniel
  Gluing compact matrix quantum groups
  arXiv:2006.13656 [math.QA, math.OA], 36 pages (2020).

• Flake, Johannes and Maaßen, Laura
  Semisimplicity and indecomposable objects in interpolating partition categories
  arXiv:2003.13798 [math.RT, math.CT, math.OA, math.QA], 29 pages (2020).

• Jung, Stefan
  Linear independences of maps associated to partitions
  arXiv:1906.10533 [math.CO], 49 pages (2019).
  

• Schmidt, Simon
  On the quantum symmetry of distance-transitive graphs
  Advances in Mathematics, Vol. 368, 107150, 15 July 2020.
  See also: arXiv:1906.06537 [math.CO, math.OA, math.QA], 43 pages (2019).
  

• Schmidt, Simon
  Quantum automorphisms of folded cube graphs
  Annales de l'Institut Fourier, Vol. 70. no. 3, 949-970, 2020.
  arXiv:1810.11284 [math.OA, math.FA], 18 pages (2018).
  

• Maaßen, Laura
  The intertwiner spaces of non-easy group-theoretical quantum groups
  to appear in Journal of Noncommutative Geometry.
  arXiv:1808.07693 [math.OA, math.GR, math.QA], 21 pages (2018).

• Gromada, Daniel
  Classification of globally colorized categories of partitions
  Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 21, No. 04, 1850029 (2018).
  See also: arXiv:1805.10800 [math.QA, math.CO], 25 pages (2018).

• Schmidt, Simon
  The Petersen graph has no quantum symmetry
  Bull. LMS, Vol. 50, Issue 3, 395-400, June 2018.
  See also: arXiv:1801.02942 [math.OA, math.FA], 7 pages (2018).

• Wahl, Jonas
  A note on reduced and von Neumann algebraic free wreath products
  Illinois J Math., Vol 59, No. 3, 801-817, 2015.
  See also: arXiv:1411.4861 [math.OA, math.QA], 14 pages (2014).

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updated: 17 November 2020   Moritz Weber

Impressum

Home Weber
Research interests What is Quantum Symmetry?
Peer reviewed publ. Monographs Preprints Further publ. Publ. by my students
      - Show abstracts
Me on GoogleScholar Me on Math Sci Net Me on arXiv
PI in SFB-TRR 195 Ed. of Analysis Math.
Faculty of Math. Saarland University