Ing. Daniel Gromada, Dr. rer. nat.

News

• [19 Aug 2022] I will speak on a masterclass The mathematics of quantum entanglement via nonlocal games in Copenhagen.
• [31 Jan 2022] I had a talk on the Research Seminar Noncommutative and Functional Analysis, Saarbrücken
• [30 Nov 2021] I had a talk on the South Atlantic Non-Commutative Seminar (online)
• [28 Sep 2021] New article on arXiv.
• [9 Sep 2021] New article on arXiv.
• [17 Jun 2021] New article on arXiv.

Teaching

Current semester

Discrete Mathematics and Graphs

Linear Algebra (CZ)

Earlier

Differential Equations and Numerical Methods (CZ) 2020/21, 2021/22

Linear Algebra (CZ) 2021/22

Research

Useful tools

• Macro package for typesetting partitions github.com/gromadan/partmac
• Some code in C++ and Singular for computing with partitions github.com/gromadan/partcat
• CMQG Wiki – encyclopedia of compact matrix quantum groups

Current projects

• Cayley graphs of finite quantum groups
• Quantum symmetries of Hadamard structures

Articles

See also my Google Scholar profile.

• Peer-reviewed

○Preprints

• Gromada, D.
  Some examples of quantum graphs
  arXiv:2109.13618 [math.QA,math-ph], 40 pages (2021).
• Gromada, D.
  Presentations of projective quantum groups
  Comptes Rendus Mathématique Vol. 360, pp. 899–907 (2022)
  arXiv:2109.04071 [math.QA], 10 pages (2021).
• Gromada, D.
  Quantum symmetries of Cayley graphs of abelian groups
  arXiv:2106.08787 [math.QA], 35 pages (2021).
• Gromada, D.
  Free quantum analogue of Coxeter group D₄
  Journal of Algebra Vol. 604, pp. 577–613 (2022)
  arXiv:2011.13242 [math.QA, math.CO], 34 pages (2020).
• Gromada, D.
  Group-theoretical graph categories
  Journal of Algebraic Combinatorics Vol. 55, pp. 591–627 (2022)
  arXiv:2009.06998 [math.QA, math.CO], 30 pages (2020–21).
• Gromada, D.
  Gluing compact matrix quantum groups
  Algebras and Representation Theory Vol. 25, pp. 53–88 (2022)
  arXiv:2006.13656 [math.QA, math.OA], 36 pages (2020).
• Gromada, D.; Weber, Moritz
  New products and Z₂-extensions of compact matrix quantum groups
  Annales de l'Institut Fourier Vol. 72, No. 1, pp. 387–434 (2022)
  arXiv:1907.08462 [math.QA, math.OA], 40 pages (2019–20).
• Gromada, D.; Weber, Moritz
  Generating linear categories of partitions
  Accepted in Kyoto Journal of Mathematics
  arXiv:1904.00166 [math.CT, math.QA], 41 pages (2019–21).
• Gromada, D.; Weber, Moritz
  Intertwiner spaces of quantum group subrepresentations
  Communications in Mathematical Physics  Vol. 376, pp. 81–115 (2020)
  arXiv:1811.02821 [math.QA, math.OA], 38 pages (2018).
• Gromada, D.
  Classification of Globally Colorized Categories of Partitions
  Infinite Dimensional Analysis, Quantum Probability and Related Topics  Vol. 21, No. 04, 1850029 (2018)
  arXiv:1805.10800 [math.QA, math.CO], 25 pages (2018).
• Gromada, D.; Pošta, Severin
  On classification of Lie algebra realizations
  arXiv:1703.00808 [math-ph,math.DG, math.RT], 20 pages (2017).
• Gromada, D.; Pošta, Severin
  Representations of Askey–Wilson algebra
  arXiv:1702.08237 [math.RT,math.QA], 19 pages (2017).
• Gromada, D.; Pošta, Severin
  Automorphisms of algebras and orthogonal polynomials
  Acta Polytechnica, Vol. 54, No. 6 (2014)

Theses

• PhD Thesis
  Compact matrix quantum groups and their representation categories
  Saarland University, Saarbrücken (2020). Supervised by Prof. Moritz Weber.
• Master's Thesis
  Classification of realizations of low-dimensional Lie algebras
  Czech Technical University, Prague (2017). Supervised by Doc. Severin Pošta.
• Bachelor's Thesis
  Ortogonální polynomy a Askeyova–Wilsonova algebra
  Czech Technical University, Prague (2015). Supervised by Doc. Severin Pošta.

Conferences, Schools, Seminars ...

2022

• 9 Sep: Polish-German seminar on quantum groups, graphs and symmetries via representation theory (online)
  Talk: Constructing simple and non-simple quantum graphs
• 15–19 August: Masterclass The mathematics of quantum entanglement via nonlocal games, Copenhagen, Denmark
  Talk: Quantum isomorphisms of graphs and quantum groups
• 24–28 May: Summer school Topological Quantum Groups, C*-Tensor Categories, and Subfactors, Waterloo, Canada
  Short talk: Quantum symmetries and deformations of Cayley graphs of abelian groups
• 31 Jan – 4 Feb: Visiting Moritz Weber at Saarland University, Saarbrücken, Germany
  Seminar talk: New examples of quantum graphs

2021

• 30 Nov: South Atlantic Non-Commutative Seminar, Buenos Aires, Argentina, on-line
  Talk: Some examples of quantum graphs
• 5 Jul: Visiting István Heckenberger at the Philipps University of Marburg, Germany
  Seminar talk: Quantum symmetries of Cayley graphs of abelian groups
• 6 Apr: Seminar of the Noncommutative Geometry and Topology Group, Prague, Czechia, on-line
  Talk: Diagrammatic categories and free quantum D₄⁺.

earlier

2020

• 22–24 Sep: Fourth annual conference of the collaborative research center SFB-TRR 195, on-line

2019

• 14–25 Oct: Visiting Adam Skalski at IMPAN, Warsaw, Poland
  Seminar talk: Z₂-extensions of compact matrix quantum groups at
  Seminar Operator algebras and quantum groups at Faculty of Physics, University of Warsaw and
  Noncommutative Geometry Seminar at Institute of Mathematics, Polish Academy of Sciences
• 9–13 Sep: Third annual meeting of the collaborative research center SFB-TRR 195, Saarbrücken, Germany
• 2–6 Sep: Around Moduli Spaces Saarbrücken, Germany
• 29 Jul – 9 Aug: Quantum groups and their analysis Oslo, Norway
  Short talk: Interpolating products of quantum groups
• 29 Apr – 3 May: Subfactors and Quantum Groups: a combinatorial approach to some problems in Operator Algebras Copenhagen, Denmark
• 21–22 Mar: Cohomology of Compact Quantum Groups and Related Topics, Besançon, France
• 18–21 Feb: Retreat SFB-TRR 195, Bad Münster am Stein, Germany
• 27 Jan – 2 Feb: Winter school of mathematical physics, Janské Lázně, Czechia
  Talk: Why should Alice and Bob study quantum groups
• 21–25 Jan: Aspects of higher representation theory: Quantum groups and categorification, Brussels, Belgium
  Short talk: Partition categories and quantum groups

2018

• 11 Dec: IRTG Seminar of SFB TRR 195, Saarbrücken, Germany
  Seminar talk: Computational aspects of partition categories
• 19–23 Nov: Visiting Gerhard Hiß at RWTH Aachen, Germany
  Seminar talk: Computational aspects of partition categories
• 8–12 Oct: Cohomology of quantum groups and quantum automorphism groups of finite graphs, Saarbrücken, Germany
  Talk: Intertwiner spaces of quantum group subrepresentations
• 24–28 Sep: Second annual meeting of the collaborative research center SFB-TRR 195, Tübingen, Germany
• 10–13 Sep: Block seminar on Game Theory, Dagstuhl, Germany
  Talk: Bimatrix games and noncooperative games
• 11–15 Jun: Quantum homogeneous spaces, Edinburgh, United Kingdom
• 6–12 May: Interactions between Operator Space Theory and Quantum Probability with Applications to Quantum Information, Oberwolfach, Germany
• 12–14 Mar: Block seminar on Combinatorial Commutative Algebra, Bingen am Rhein, Germany
  Talk: Introduction to homological algebra and graded algebras
• 1 Mar: MAFIA Seminar FNSPE CTU, Prague, Czechia
  Seminar talk: Easy compact matrix quantum groups
• 22–26 Jan: Workshop Tensor categories, Hopf algebras and quantum groups, Marburg, Germany

2017

• 25–28 Sep: First annual meeting of the collaborative research center SFB-TRR 195, Aachen, Germany
  Talk: Classifying categories of words
• 4–8 Sep: Mathematical Aspects of Quantum Information, Cargèse, France
• 22–28 Jan: Winter school of mathematical physics, Janské Lázně, Czechia
  Talk: Classification of Lie algebra realizations

2016

• 4–9 Jul: V School of Geometry and Physics, Białowieża, Poland
• 26 Jun – 7 Jul: XXXV Workshop on Geometric Methods in Physics, Białowieża, Poland
  Poster: Construction of Lie algebra realizations
• 12–17 Jun: Group Analysis of Differential Equations and Integrable Systems, Larnaca, Cyprus
  Talk: Orthogonal polynomials and Askey–Wilson algebra
• 23–24 May: Combinatoris on words and mathematical physics, Prague, Czechia
  Talk: Construction of Lie algebra realizations
• 24–30 Jan: Winter school of mathematical physics, Janské Lázně, Czechia
  Talk: Construction of realizations of Lie algebras

2015

• 17–22 Aug: Methods of algebra and functional analysis in applications, Telč, Czechia
  Talk: Algebras and orthogonal polynomials

2014

• 18–24 May: Combinatorics on Words and Mathematical Physics, Kruh u Jilemnice, Czechia

2013

• 29 Jul – 3 Aug: International School on Integrable Systems and Quantum Symmetry, Dubna, Russia