# Daniel Gromada

Assistant Professor

22435 5121

JP:B-520a

## News

- [17–21 Jan 2025] I am coorganizing a Workshop on Quantum Graphs in Saarbrücken, Germany

## Teaching

#### Current semester

Differential Equations and Numerical Methods (CS)

#### Earlier

Discrete Mathematics and Graphs 2022/23, 2023/24

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

Linear Algebra (CS) 2021/22, 2022/23

## 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

### Articles

See also my Google Scholar profile.• Peer-reviewed | ○Preprints |

- G., Quantum association schemes. arXiv:2404.06157, 33 pages (2024)
- G., Quantum symmetries of Hadamard matrices,
*Trans Am Math Soc*. - G., Some examples of quantum graphs,
*Lett Math Phys***112**, 121 (2022) - G., Presentations of projective quantum groups,
*Comptes Rendus Math***360**, 899–907 (2022) - G., Quantum symmetries of Cayley graphs of abelian groups,
*Glasgow Math J*,**65**(3), 655--686 (2023) - G., Free quantum analogue of Coxeter group
*D*_{4},*J Algebra***604**, 577–613 (2022) - G., Group-theoretical graph categories,
*J Algebr Comb***55**, 591–627 (2022) - G., Gluing compact matrix quantum groups,
*Algebras Represent Th***25**, pp. 53–88 (2022) - G., Weber M., New products and Z
_{2}-extensions of compact matrix quantum groups,*Ann I Fourier***72**(1), 387–434 (2022) - G., Weber M., Generating linear categories of partitions
*Kyoto J Math***62**(4) 865–909 (2022) - G., Weber M., Intertwiner spaces of quantum group subrepresentations,
*Comm Math Phys***376**, 81–115 (2020) - G., Classification of Globally Colorized Categories of Partitions,
*Inf Dim Anal Qu*,**21**(04), 1850029 (2018) - G., Pošta S., On classification of Lie algebra realizations, arXiv:1703.00808 [math-ph,math.DG, math.RT], 20 pages (2017).
- G., Pošta S., Representations of Askey–Wilson algebra, arXiv:1702.08237 [math.RT,math.QA], 19 pages (2017).
- G., Pošta S., Automorphisms of algebras and orthogonal polynomials,
*Acta Polytech*,**54**(6), 394--397 (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 ...

#### 2024

- 17 Jun: QGS: Quantum Groups Seminar
*(online)*

Talk: Cayley graphs: Symmetries, quantizations, duality - 19 Mar: Non-local games seminar, Copenhagen, Denmark
*(online)*

Talk: Quantum symmetries of quantum channels - 15 Jan: Geometric Methods in Mathematics, Dresden, Germany

Talk: Quantum symmetries and diagrammatic categories

#### 2023

- 9–11 Oct: German-Polish Workshop on Quantum groups, graphs and symmetries, Warsaw, Poland

Talk: Quantum symmetries and diagrammatic categories - 25 Sep: Virtual Algebraic Graph Theory Seminar, Waterloo, Canada

Talk: Quantum symmetries of Hadamard matrices - 11–15 Sep:Quantum Groups and Noncommutative Geometry in Prague, Czechia

Talk: Quantum symmetries of things - 30 Jan: Combinatorics seminar at U. Winsconsin–Madison, USA,
*on-line*

Talk: Quantum symmetries of graphs

#### 2022

- 15–17 Nov: Mini workshop on quantum groups, graphs and symmetries via representation theory

Talk: Quantum symmetries of Hadamard matrices - 9 Sep: Polish-German seminar on quantum groups, graphs and symmetries via representation theory,
*on-line*

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