Publications

Show abstracts

Preprints

• 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

• 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

• 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).