Urban Jezernik
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.
Publications
Two-generation of traceless matrices over finite fields (with Omer Cantor, Andoni Zozaya) preprint [arxiv]
Irrationality of generic quotient varieties via Bogomolov multipliers (with Jonatan Sánchez) IMRN (2023) [arxiv]
Babai's conjecture for high-rank classical groups with random generators (with Sean Eberhard) Invent. Math. 227 (2022) [arxiv]
On surjectivity of word maps on PSL2 (with Jonatan Sánchez) J. Algebra 587 (2021) [arxiv, code]
Gaps in probabilities of satisfying some commutator-like identities (with Costantino Delizia, Primož Moravec, Chiara Nicotera) Israel J. Math. 237 (2020) [arxiv]
Bogomolov multipliers of p-groups of maximal class (with Gustavo Adolfo Fernandez-Alcober) Q. J. Math. 71 (2020) [arxiv]
Commuting probability (expository, in Slovenian) Obz. mat. fiz. 65 (2018) [pdf]
Commutativity preserving extensions of groups (with Primož Moravec) Proc. Roy. Soc. Edinburgh Sect. A. 148 (2018) [arxiv]
Groups in which every non-abelian subgroup is self-normalized (with Costantino Delizia, Primož Moravec, Chiara Nicotera) Monatsh. Math. 185 (2018) [arxiv]
Groups in which every non-nilpotent subgroup is self-normalizing (with Costantino Delizia, Primož Moravec, Chiara Nicotera) Ars Math. Contemp. 15 (2018) [arxiv]
Units of group rings, the Bogomolov multiplier, and the fake degree conjecture (with Javier Garcia-Rodriguez, Andrei Jaikin-Zapirain) Math. Proc. Camb. Phil. Soc. 163 (2017) [arxiv]
Locally finite groups in which every non-cyclic subgroup is self-centralizing (with Costantino Delizia, Primož Moravec, Chiara Nicotera, Chris Parker) J. Pure Appl. Algebra 221 (2017) [arxiv]
Universal commutator relations, Bogomolov multipliers, and commuting probability (with Primož Moravec) J. Algebra 428 (2015) [arxiv]
Groups in which every non-cyclic subgroup contains its centralizer (with Costantino Delizia, Primož Moravec, Chiara Nicotera) J. Algebra Appl. 13 (2014) [arxiv]
Bogomolov multipliers of groups of order 128 (with Primož Moravec) Exp. Math. 23 (2014) [arxiv]
Schur multipliers of unitriangular groups J. Algebra 399 (2014) [arxiv]
Universal Commutator Relations (PhD thesis) University of Ljubljana (2016) [pdf]
Teaching
Current: Discrete structures, Elementary number theory
Past: Representation theory, Group theory, Computer tools in mathematics, Expander graphs
Student supervision
BSc: Matevž Miščič: Shuffling by random transpositions (2022), Tim Milanez: Walks with random permutations (2022), Matej Cerar: Diameter of the group SL2(Fp) (2022)
MSc: Saša Trstenjak: The Hasse principle (2022), Barbara Bone: Sets of integers without three-term arithmetic progressions (2024)
Activities
Coordinator of a Reading group on various advanced topics
Head of organization committee for the summer school Mathematics in Ljubljana 2023
Coorganizer of the conference Young Geometric Group Theory VIII (2019)
Coorganizer of the conference GTA: Gran Bilbao 2019
Minicourse Computational group theory with GAP at the University of the Basque Country (2018)
Grants and Awards
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) [youtube]
Marie Skłodowska-Curie Individual Fellowship BogomolovMultiplier (2017)
Reinhold Baer Prize for outstanding PhD thesis in group theory (2017)