Division of Algebra and Number Theory – Fakultet za matematiku

Chair:

Assoc. Prof. Ana Jurasić

Members:

Prof. Predrag Dominis Prester
Assoc. Prof. Tajana Ban Kirigin
Assoc. Prof. Sanda Bujačić Babić
Assoc. Prof. Marijana Butorac
Assoc. Prof. Ana Jurasić
Assoc. Prof. Vera Tonić
Assist. Prof. Nevena Jurčević Peček

Division of Algebra and Number Theory was founded in late 2010 by dividing up the former Division of Algebra and Discrete Mathematics.

Science

The scientific activity of the Division members is in the areas of algebra, number theory, mathematical analysis, geometry and topology, computer science, and theoretical physics of elementary particles. In particular, the Division members’ area of research interests includes:

Langlands program, automorphic forms
Representation theory
Affine Lie algebras and vertex operator algebras
Diophantine equations and polynomial variants of the problem of Diophantus
Dimension theories, resolution theorems
Geometric group theory
Formal models of collaboration systems, analysis of the security protocols
Quantum field theory,
Classical and quantum gravity and theories of unification of forces.

Members of the Division actively participate in the international scientific community by collaborating with scientists from different countries, participating and presenting at international scientific conferences and seminars, visiting prestigious international institutions, lecturing at foreign doctoral studies and doctoral and postdoctoral summer schools, reviewing books and articles for relevant mathematical literature databases, evaluating articles submitted for publication in international journals, and evaluating doctoral dissertations at prestigious international institutions.

Members of the Division participate in the implementation of the Croatian Doctoral Program in Mathematics (joint program of J.J. Strossmayer University of Osijek, University of Rijeka, University of Split, University of Zagreb).

Marijana Butorac is a member of the mathematical research unit the Scientific Center of Excellence for Quantum and Complex Systems, and Representations of Lie Algebras – QuantiXLie, led by Prof. Hrvoje Buljan and Prof. Pavle Pandžić.

Active Research Projects

Afine Liejeve algebre i kvantne grupe, HRZZ project (project leader: Assoc. Prof. Marijana Butorac) (31.12.2025. – 30.12.2028.)
Matematičko modeliranje u umjetnoj inteligenciji (project leader: Assoc. Prof. Sanda Bujačić Babić) (01.10.2025. – 01.10.2029.)
Posebni problemi u algebarskim strukturama u teoriji brojeva i topologiji (project leader: Assoc. Prof. Ana Jurasić) (01.10.2025. – 01.10.2029.)
Kvantna teorija polja, gravitacija i ujedinjenje sila (project leader: Prof. Predrag Dominis Prester, uniri-iz-25-237) (01.10.2025. – 01.10.2029.)
Formalni sistemi i modeliranje (FORMALS-2) (project leader: izv. prof. dr. sc. Tin Perkov) za razdoblje 2024. – 2027.
Teorija brojeva i aritmetička geometrija (project leader: prof. dr. sc. Filip Najman) (2023. – 2027.)
Fundamental challenges in theoretical physics (Predrag Dominis Prester is a member of Board of Directors), EU COST-action project CA22113 (2023.-2027.)

Finished Research Projects

Matematičko modeliranje u obradi prirodnog jezika (project leader: Assoc. Prof. Sanda Bujačić Babić, uniri-iskusni-prirod-23-150), 2023. – 2025.
Algebarske strukture i njihove primjene u teoriji brojeva i topologiji (project leader: Assoc. Prof. Ana Jurasić, uniri-iskusni-prirod-23-66), 2023. – 2025.
Kvantna teorija polja, gravitacija i teorije viših spinova (project leader: Prof. Predrag Dominis Prester, uniri-iskusni-prirod-23-222), 2023. – 2025.
Automorfne forme, reprezentacije i primjene (project leader: Prof. Goran Muić),
Croatian Science Foundation research project no 9364, 2014. – 2018.
Algebarske i kombinatorne metode u teoriji verteks algebri (project leader: Prof. Dražen Adamović),
Croatian Science Foundation research project 2634, 2014. – 2018.
Diofantske m-torke, eliptičke krivulje, Thueove i jednadžbe indeksnog oblika (project leader: Prof. Andrej Dujella), Croatian Science Foundation research project 6422, 2014. – 2018.
Cyber Protocols in the Physical Environment (project leader A. Scedrov), Office of Naval Research (ONR), USA, 2015. – 2018.
Foundations of geometric approximate group theory, (project leader: Tobias Hantrick, KIT Karlsruhe, Germany) , 2017. – 2023.
Formalno rasuđivanje i semantike (FORMALS), UIP-05-2017-9219, project leader: Tin Perkov, Croatian Science Foundation research project, 2017. – 2022.
Diofantska geometrija i primjene, project leader: Matija Kazalicki, Croatian Science Foundation research project, 2018. – 2022.
Izlučivanje ključnih riječi i sažimanje tekstova na temelju reprezentacije u mrežama jezika – LangNet, project leader: Prof. Sanda Martinčić-Ipšić, UNIRI Research Project, 2019. – 2021.
Jezično izražavanje emocija: Računalni resusi, metode identifikacije i ontološko modeliranje komunikacije psiholoških stanja (EmoCNet), project leader: Assoc. Prof. Benedikt Perak, UNIRI Research Project, 2019. – 2021.
Kvantna teorija polja, gravitacija i unifikacija sila, project leader: Prof. Predrag Dominis Prester, UNIRI Research Project, uniri-prirod-18-256, 2019. – 2023.
Security for resource limited networked Cyber-physical systems, ONR, USA, 2020. – 2023.
Quantum Current Algebras and Their Representation Theory, project leader: Assoc. Prof. Slaven Kožić, Croatian Science Foundation installation research project UIP-2019-04-8488, 2020. – 2024.

Selected Research Papers

Ban Kirigin, T.; Bujačić Babić, S. Semi-Local Integration Measure for Directed Graphs, Mathematics (2024), 12, 1087, doi:10.3390/math12071087,
Alturki, Musab A.; Ban Kirigin, Tajana; Kanovich, Max; Nigam, Vivek; Scedrov, Andre; Talcott, Carolyn On the Formalization and Computational Complexity of Resilience Problems for Cyber-Physical Systems // Lecture notes in computer science, 2022. str. 96-113. doi: 10.1007/978-3-031-17715-6_8,
Ban Kirigin, Tajana; Bujačić Babić, Sanda; Perak, Benedikt Lexical Sense Labeling and Sentiment Potential Analysis using Corpus-Based Dependency Graph, Mathematics, 9 (2021), 12; 1449, 22, doi:10.3390/math9121449,
Urquiza, Abraão Aires; Alturki, Musab A.; Kanovich, Max; Ban Kirigin, Tajana; Nigam, Vivek; Scedrov, Andre; Talcott, Carolyn Resource and Timing Aspects of Security Protocols // Journal of computer security, 29 (2021), 3; 299-340. doi: 10.3233/JCS-200012
M. Kanovich, T. Ban Kirigin, V. Nigam, A. Scedrov, C. Talcott, R. Perovic, A rewriting framework and logic for activities subject to regulations. Mathematical structures in computer science 27(3) (2017) 332-375.
M. Kanovich, T. Ban Kirigin, V. Nigam, A. Scedrov, and C. Talcott, Time, Computational Complexity, and Probability in the Analysis of Distance-Bounding Protocols, Journal of Computer Security, 25(6): 585-630, 2017.
Bliznac Trebješanin, M. and Bujačić Babić, S., Polynomial (4)-quadruples over Gaussian integers, Glasnik Matematički, Vol. 59, No. 1 (2024), 1-31, doi.org:10.3336/gm.59.1.01
L. Bonora ; M. Cvitan ; P. Dominis Prester ; S. Giaccari ; M. Paulišić, Axial gravity: a non-perturbative approach to split anomalies, Eur. Phys. J.C 78 (2018) 8, 652. doi: 10.1140/epjc/s10052-018-6141-1
L. Bonora ; M. Cvitan ; P. Dominis Prester ; S. Giaccari ; M. Paulišić, Worldline quantization of field theory, effective actions and L_infty structure, JHEP 2018 (2018) 095.
L. Bonora ; M. Cvitan ; P. Dominis Prester ; A. Duarte Pereira ; S. Giaccari, Axial gravity, massless fermions and trace anomalies, Eur. Phys .J. C 77 (2017) 8, 511.
Bujačić Babić, Sanda; Nabardi, Kamran, On Some Diophantine Equations, Miskolc Mathematical Notes, 22 (2021), 1; 65-75
M. Butorac, C. Sadowski, Combinatorial bases of principal subspaces of modules for twisted affine Lie algebras of type A_2l-1, D_l⁽²⁾, E₆⁽²⁾, and D₄⁽³⁾, New York J. Math. 25 (2019) 71-106.
M. Butorac, N. Jing, S. Kožić, h-adic quantum vertex algebras associated with rational R-matrix in types B, C and D, Lett. Math. Phys. 109 (2019), 2439-2471.
M. Butorac, Quasi-particle bases of principal subspaces for the affine Lie algebra of type G₂⁽¹⁾, Glas. Mat. Ser. III 52 (2017), 79-98.
M. Cvitan ; P. Dominis Prester ; S. Giaccari ; M. Paulišić ; I, Vuković, Gauging the higher-spin-like symmetries by the Moyal product, JHEP 2021 (2021) 144.
Matthew Cordes, Tobias Hartnick, Vera Tonić, Foundations of geometric approximate group theory, 2024. prihvaćeno za objavljivanje u Memoirs of the American Mathematical Society
A. Filipin, A. Jurasić, On the existence of D(-3)-quadruples in Z[X], Glasnik matematički, 57(77) (2022), 203-219.
A. Filipin, A. Jurasić, A polynomial variant of a problem of Diophantus and its consequences, Glasnik matematički, 54 (2019), 1; 21-52.
C. Fuchs, A. Jurasić, R. Paulin, Elementary resolution of a family of quartic Thue equations over function fields, Monatsh. Math., 180 (2016), 2; 205-211.
N. Grbac, N. Jurčević Peček, Note on reducibility of parabolic induction for hermitian quaternionic groups over p-adic fields, Mathematical communications, 23 (2018), 2; 181-196.
Tobias Hartnick, Vera Tonić, Hurewicz and Dranishnikov-Smith theorems for asymptotic dimension of countable approximate groups, Topology and its Appls. 349 (2024),
Vera Tonić, A Hurewicz-type formula for asymptotic-dimension-lowering symmetric quasimorphisms of countable approximate groups, Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 283-297.
Vera Tonić, A Hurewicz-type theorem for quasimorphisms of countable approximate groups, Topology and its Applications, Volume 381 (2026), paper no. 109744.

Research Class

Members of the Division participate in the organisation and delivery of research seminars within the Research Class of the Division of Algebra and Number Theory at the Faculty of Mathematics. Within the framework of the Research Class seminars, invited speakers and members of the Division present their current research results, as well as other relevant topics in the field.

Given the breadth and diversity of the research interests pursued by members of the Division, these lectures and discussions foster the exchange of ideas and encourage potential research collaboration both within the Division and more broadly.

The initiative to establish this research activity was formally proposed at the Division meeting held on 17 February 2020. Owing to circumstances related to the COVID-19 pandemic, the first Research Class seminar was held on 16 March 2022.

Research Class Chair: Assoc. Prof. Sanda Bujačić Babić

Seminars:

25.03.2022. Tajana Ban Kirigin, Sanda Bujačić Babić, Benedikt Perak: Multidisciplinarni pristup u digitalnoj lingvistici
29.04.2022. Marijana Butorac, Slaven Kožić: Glavni potprostori kvantne afine verteks-algebre tipa A1(1)
27.05.2022. Zvonimir Šikić: Matematika i slikarstvo
28.10.2022. Sanda Bujačić Babić: O regularnosti D(4)-četvorki iz Z[i][X]
09.12.2022. Vera Tonić: Asimptotička dimenzija i primjena na geometrijsku teoriju aproksimativnih grupa, part one
20.01.2023. Vera Tonić: Asimptotička dimenzija i primjena na geometrijsku teoriju aproksimativnih grupa, part two
10.03.2023. Ana Jurasić: Polinomne varijante Diofantova problema
01.12.2023. Predrag Dominis Prester: Matematika Standardnog modela i izvan njega
09.02.2024. Daniel Leoni: Skok u ocean podataka (iOlap)
08.04.2024. Leonard R. Rubin: What is the dimension of space?
24.05.2024. Zvonimir Šikić: Wignerov problem i realni brojevi
07.06.2024. Vera Tonić: Teoremi Hurewiczevog tipa – od opće topologije do aproksimativnih grupa
11.06.2025. Moshe Cohen: Randomness in Topology
12.06.2025. Tin Adlešić: Zermelova aksiomatizacija teorije skupova
07.11.2025. Dijana Ilišević: Od izometrija do izomorfizama
10.-11.11.2025. Zvonimir Šikić: O brojevima – konačnim i beskonačnim (series of lectures)

It is worth highlighting that a member of the Division, Sanda Bujačić Babić, is a co-author of the book Diophantine Analysis (together with Alan Filipin, Simon Kristensen, Tapani Matala-aho, and Nicola M.R. Oswald), published in 2016 by the prestigious publisher Springer.

Teaching

The Division of Algebra and Number Theory is involved in the organisation and delivery of all degree programmes offered by the Faculty of Mathematics, as well as in providing mathematics instruction for selected programmes delivered by other constituent units of the University of Rijeka.

Members of the Division have designed and developed a number of courses within these programmes and work collaboratively with colleagues across the Faculty on the continuous development and implementation of individual courses, with the aim of enhancing programme quality and strengthening coherence across the curriculum. In addition to courses in algebra and number theory, this includes courses in other areas of mathematics that are, to varying degrees, relevant to number theory.

A member of the Division, Prof. Predrag Dominis Prester, serves as the course coordinator for the doctoral-level course Black Hole Physics within the PhD programme in Physics.

Public Engagement and Professional Activities

Members of the Division are authors and lecturers of numerous outreach lectures and workshops designed for primary and secondary school students, with the aim of promoting mathematics and mathematics studies. They also actively contribute to the work of professional and alumni associations, including the Society of Mathematicians and Physicists, the MatRi Alumni Club, and the Croatian Mathematical Society.

Division members regularly participate in public lectures and workshops as part of major outreach events in Rijeka and beyond, such as the Science Festival, the Evening of Mathematics, and the Open Days of the Faculty of Mathematics.

In 2017, at the Rijeka Mathematical Meetings under the theme The Deepest Secrets of Mathematics, lectures and workshops were delivered by members of the Division.

In 2025, at the Rijeka Mathematical Meetings under the theme Mathematics Around Us, lectures and workshops were likewise delivered by members of the Division.