Department of Mathematics
Faculty of Mathematics and Physics
University of Ljubljana
urban.jezernik AT fmf.uni-lj.si
I am an assistant professor at the Faculty of Mathematics and Physics at the University of Ljubljana in Slovenia, where I also serve as the coordinator of the BSc programme.
From 2019 to 2021, I was a postdoctoral fellow at the Alfréd Rényi Institute of Mathematics in Budapest, working in the research group of László Pyber. From 2017 to 2019, I was a Marie Skłodowska-Curie postdoctoral fellow at the University of the Basque Country in the GTA research group. I completed my PhD in 2016 at the University of Ljubljana under the supervision of Primož Moravec. During my graduate studies, I spent a semester at the University of Toronto visiting Sanja Fidler and Raquel Urtasun, and I spent a year at the Institute of Mathematical Sciences ICMAT in Madrid visiting Andrei Jaikin-Zapirain.
Diameter bounds for finite simple Lie algebras (with Marco Barbieri, Matevž Miščič)
preprint (2025) [arxiv]
Additive diameters of group representations (with Špela Špenko)
preprint (2025) [arxiv]
Random Lie bracket on sl2(Fp) (with Matevž Miščič)
preprint (2025) [arxiv]
Two-generation of traceless matrices over finite fields (with Omer Cantor, Andoni Zozaya)
Linear Algebra and its Applications (2025) [journal, arxiv]
Irrationality of generic quotient varieties via Bogomolov multipliers (with Jonatan Sánchez)
International Mathematics Research Notices (2023) [journal, arxiv, video]
Babai's conjecture for high-rank classical groups with random generators (with Sean Eberhard)
Inventiones Mathematicae (2022) [journal, arxiv, video]
On surjectivity of word maps on PSL2 (with Jonatan Sánchez)
Journal of Algebra (2021) [journal, arxiv, code]
Gaps in probabilities of satisfying some commutator-like identities (with Costantino Delizia, Primož Moravec, Chiara Nicotera)
Israel Journal of Mathematics (2020) [journal, arxiv]
Bogomolov multipliers of p-groups of maximal class (with Gustavo Adolfo Fernandez-Alcober)
The Quarterly Journal of Mathematics (2020) [journal, arxiv]
Commuting probability (expository, in Slovenian)
Obzornik za matematiko in fiziko (2018) [journal, pdf]
Commutativity preserving extensions of groups (with Primož Moravec)
Proceedings of the Royal Society of Edinburgh Section A (2018) [journal, arxiv]
Groups in which every non-abelian subgroup is self-normalized (with Costantino Delizia, Primož Moravec, Chiara Nicotera)
Monatshefte fur Mathematik (2018) [journal, arxiv]
Groups in which every non-nilpotent subgroup is self-normalizing (with Costantino Delizia, Primož Moravec, Chiara Nicotera)
Ars Mathematica Contemporanea (2018) [journal, arxiv]
Units of group rings, the Bogomolov multiplier, and the fake degree conjecture (with Javier Garcia-Rodriguez, Andrei Jaikin-Zapirain)
Mathematical Proceedings of the Cambridge Philosophical Society (2017) [journal, arxiv]
Locally finite groups in which every non-cyclic subgroup is self-centralizing (with Costantino Delizia, Primož Moravec, Chiara Nicotera, Chris Parker)
Journal of Pure and Applied Algebra (2017) [journal, arxiv]
Universal commutator relations, Bogomolov multipliers, and commuting probability (with Primož Moravec)
Journal of Algebra (2015) [journal, arxiv]
Groups in which every non-cyclic subgroup contains its centralizer (with Costantino Delizia, Primož Moravec, Chiara Nicotera)
Journal of Algebra and Its Applications (2014) [journal, arxiv]
Bogomolov multipliers of groups of order 128 (with Primož Moravec)
Experimental Mathematics (2014) [journal, arxiv]
Schur multipliers of unitriangular groups
Journal of Algebra (2014) [journal, arxiv]
Universal Commutator Relations (PhD thesis)
University of Ljubljana (2016) [repozitorij, pdf]
Present and future:
Past:
Mathematics in Ljubljana (2023, 2024, 2025)
Young Geometric Group Theory VIII (2019)
Computational group theory with GAP (2018)
2025/26: Linear algebra, Representation theory
Past: Expander graphs, Discrete structures, Elementary number theory, Group theory, Computer tools in mathematics
BSc:
Matevž Miščič: Shuffling by random transpositions (2022)
Tim Milanez: Walks with random permutations (2022)
Matej Cerar: Diameter of the group SL2(Fp) (2022)
Jaša Knap: Short group laws (2024)
Timotej Mlakar: Algebraic signal processing theory and spectral analysis algorithms (2025)
MSc:
Saša Trstenjak: The Hasse principle (2022)
Barbara Bone: Sets of integers without three-term arithmetic progressions (2024)
Filip Rus: Calculating digits of pi (2024) [Franc Močnik award]
Tadej Petrič: Ramanujan graphs (2025)
Miloš Puđa: Local permutation stability of groups (2025)
PhD:
Matevž Miščič (2024—)
Postdoc:
Andoni Zozaya (2023—2025)
Marco Barbieri (2025—)
ARIS research project Rapid random generation of Lie algebras J1-50001(2023)
Honorary plaque for young university professors at the University of Ljubljana (2023)
Paper on Babai's conjecture awarded Top 10 most outstanding research achievements of the University of Ljubljana (2021) [video]
Marie Skłodowska-Curie Individual Fellowship BogomolovMultiplier (2017)
Reinhold Baer Prize for outstanding PhD thesis in group theory (2017)