# Ing. Daniel Gromada, Dr. rer. nat.

Assistant Professor

22435 5121

JP:B-520a

## 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

#### 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*D*_{4}

*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 Z_{2}-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 D*._{4}^{+}

## 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:*Z*at_{2}-extensions of compact matrix quantum groups

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