Topics

For decades, scientists have been looking for a unified theory of all fundamental forces of nature. Even though there have been many important and illuminating ideas, the final answer to this question is still out of sight.
We are however sure that at the scales where both the quantum phenomena and curvature of the space time play a significant role, our standard physical notions and approaches need to be changed.
Our team works on topics related to the search of these new notions and approaches. Most notably problems in noncommutative geometry, fuzzy field theory and mathematical objects in the formulation of string theory.

Grants

Members of the group are currently supported by:

• VEGA 1/0025/23 - /i>Matrix models and quantum gravity
• COST Action CA21109 - CaLISTA,
• CEEPUS RS-1514-05-2425 network - Quantum Spacetime, Gravitation and Cosmology
• the Department of theoretical physics, FMFI UK,
• Anton Zajac.

Recent publications

Our most recent publications and preprints are:

• M. Hrmo, S. Kováčik, P. Rusnák, J. Tekel - Hydrogen Atom in a Fuzzy Spherical Cavity
  arXiv
• B. Bukor, J. Tekel - Cubic asymmetric multitrace matrix model
  arXiv
• S. Kováčik - Expanding microscopic black holes
  Int. J. Mod. Phys. D 33 (2024), arXiv
• S. Kováčik, M. Ďurišíková, P. Hrmo - Phenomenology of the dispersion law in a three-dimensional quantum space
  Int. J. Mod. Phys. A 40 (2025) 01, arXiv
• S. Kováčik, J. Tekel - Fuzzy onionlike space as a matrix model
• B. Bukor, J. Tekel - On quarkonium masses in 3D non-commutative space
  Eur. Phys. J. Plus 138, 499 (2023), arXiv
• D. Prekrat, D. Ranković, N. K. Todorović-Vasović, S. Kováčik & J. Tekel - Approximate treatment of noncommutative curvature in quartic matrix model
  JHEP 01 (2023) 109, arXiv

Teaching

Teaching is an integral part of our work at the Comenius University. Our members give several important courses in the graduate and post-graduate programs. For more information see the program websites.

• April 2025 (a busy month :) )
  Benedek Bukor gave a talk about some of our research at CIRM conference in Marseille.
• April 2025
  Juraj and Samuel successfully gave their habilitation lectures and defended their habilitation theses as the final hurdle on their way to become associate professors.
• April 2025
  We had the pleasure of hosting Jan Pulmann again, now of University of Edinburgh, who gave a seminar titled "Lagrangian relations, half-densities and quantum L Infinity algebras". Notes from his presentation are available here.
• October 2024
  We had pleasure of hosting our colleagues from CaLISTA action at a small workshop meeting.
• September 2024
  Many members of our group attended CORFU meeting and presented their work, where Juraj is one of the organizers.
• May 2024
  Juraj gave an invited public talk at the general meeting of the CaLISTA action in Sofia.
• May 2024
  We had the pleasure of hosting our colleague Dragan Prekrat from University of Belgrade for a short visit.
• March 2024
  The final report of the grant "Quantum structure of Spacetime", where Juraj Tekel was the principal investigator and all the members of our group were a part of the research team, has been accepted and the grant has been closed as successful. Moreover, it was evaluated as a grant that has achieved significant and important results by the agency.
• January 2024
  We had the pleasure of hosting Professor Peter Schupp of the Constructor University in Bremen. Peter gave a seminar talk titled "An algebraic formulation of nonassociative quantum mechanics", slides available here.
• September 2023
  We are very happy to welcome Eugenia Boffo as a new member of the group!
• April 2020
  We are very happy to let you know that our grant proposal "Matrix models and quantum gravity" has been accepted by the VEGA agency.
• September 2022
  We are very happy to welcome Martin Krššák as a new member of the group!
• Summer 2022
  Mária Šubjaková has successfully defended her thesis and received the degree PhD. Congratulations!
• Summer 2021
  After a long time in social isolation, members of our group have taken part in several in person events over the summer. Including presentations of their work, most importantly a series of invited lectures at Summer school on theoretical physics and an invited talk at the Cofu Summer Institute 2021.
• October 2020
  We are very happy to welcome Samuel Kováčik as a new member of the group!
• Jun 2020
  Paper "Second moment fuzzy-field-theory-like matrix models" by members of the group Mária Šubjaková and Juraj Tekel has been published in the Journal of High Energy Physics!
• April 2020
  We are very happy to let you know that our grant proposal "Quantum structure of spacetime" has been accepted by the VEGA agency.
• March 2020
  Juraj Tekel has given a talk aimed at general public at SPACE::TALK event in Košice. More info here (in slovak).
• February 2020
  The final report of the grant "Towards the unification of quantum field theory and gravity in the new physics", where Peter Prešnajder was the principal investigator and all the members of our group were a part of the research team, has been accepted and the grant has been closed as successful.
• December 2019
  We had the pleasure of hosting Jan Pulmann, University of Geneva, who gave a seminar titled "Dualities in the Batalin-Vilkovisky formalism". Notes from his presentation are available here.