Division of Algebra and Number Theory
Chair:
Assist. Prof. Ana Jurasić
Members:
 Assist. Prof. Tajana Ban Kirigin
 Assist. Prof. Sanda Bujačić Babić
 Assist. Prof. Marijana Butorac
 Assist. Prof. Ana Jurasić
 Assist. Prof. Vera Tonić
 Sen. Lecturer Rene Sušanj
 Dr. Nevena Jurčević Peček
 Bojan Ostić
Division of Algebra and Number Theory was founded in late 2010 by dividing up the former Division of Algebra and Discrete Mathematics. The Division has 8 members, four of which are holding tenure track positions, two senior teaching assistants, one senior lecturer and one teaching assistant.
Science
Research articles of the members of the Division pertain to the areas of algebra, number theory, mathematical analysis, geometry and topology and computing. 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 versions of the problem of Diophantus
 Dimension theories, resolution theorems
 Geometric group theory
 Formal models of collaboration systems, analysis of the security protocols
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).
Active research projects in which members of the Division participate:
 Foundations of geometric approximate group theory (principal investigator: Tobias Hantrick) , project based on the Giessen University in Germany during 2018
 Formal Reasoning and Semantics (FORMALS) UIP0520179219 (principal investigator: Tin Perkov), for the period 20172022
 Keyword Extraction and Summarization Based on Language Networks LangNet (principal investigator: Sanda MartinčićIpšić), University of Rijeka grant for the period 20192021
 Conceptual network of the linguistic expression of emotions and affective states (EmoCNet) (principal investigator: Benedikt Perak), University of Rijeka grant for the period 20192021
 Diophantine geometry and applications (principal investigator: Matija Kazalicki), Croatian Science Foundation grant for the period 20182022
Finished research projects in which members of the Division participated during the last five years:

Algebraic and analytic Methods in Number Theory (principal investigator: Neven Grbac),
University of Rijeka research grant no. 13.14.1.2.02 for the period 20132015  Classical problems of Diophantus, Fermat and Ritt using New analytical and Algebraic Techniques (principal investigators: Christian Elsholtz and Alan Filipin), bilateral cooperation project of Croatia and Austria for the period 2016.2017.
 Automorphic Forms, Representations and Applications (principal investigator: Goran Muić), Croatian Science Foundation research grant no. 9364 for the period 20142018
 Algebraic and Combinatorial Methods in Vertex Algebra Theory (principal investigator: Dražen Adamović), Croatian Science Foundation research grant no. 2634 for the period 20142018
 Diophantine mtuples, Elliptic Curves, Thue and Index Form Equations (principal investigator: Andrej Dujella), Croatian Science Foundation research grant no. 6422 for the period 20142018
 Regulated Collaborative Systems: Foundations and Applications (principal investigator: V. Nigam), Research Without Borders project (Brazil) for the period 20132016
 Cyber Protocols in the Physical Environment (principal investigator: A. Scedrov), Office of Naval Research (ONR), USA, for the period 20162017
 Complex Language Networks LangNet (principal investigator: Sanda MartinčićIpšić), University of Rijeka initial research grant no.13.13.2.2.07 for the period 20142017
 Cohomology of Arithmetic Groups and Automorphic Forms (principal investigators: Neven Grbac and Joachim Schwermer), bilateral cooperation project of Croatia and Austria for the period 20142015
Selection of research papers:
 A. Filipin, A. Jurasić, A polynomial variant of a problem of Diophantus and its consequences, Glasnik matematički, 54 (2019), 1; 2152.
 N. Grbac, N. Jurčević Peček, Note on reducibility of parabolic induction for hermitian quaternionic groups over padic fields, accepted for publication, Mathematical communications
 S. Bujačić, A variation of a congruence of Subbarao for n=2^{α}5^{β}, α, β≥0, accepted for publication, Periodica Mathematica Hungarica
 M. Butorac, C. Sadowski, Combinatorial bases of principal subspaces of modules for twisted affine Lie algebras of type A_{2l1}, D_{l}^{(2)}, E_{6}^{(2)}, and D_{4}^{(3)}, New York J. Math. 25 (2019) 71106.
 M. Butorac, N. Jing, S. Kožić, hadic quantum vertex algebras associated with rational Rmatrix in types B, C and D, Lett. Math. Phys. (to appear).
 M. Butorac, Quasiparticle bases of principal subspaces for the affine Lie algebra of type G_{2}^{(1)}, Glas. Mat. Ser. III 52 (2017), 7998.
 I. Ciganović, N. Grbac, The Zelevinsky classification of unramified representations of the metaplectic group, J. Algebra 454 (2016), 357–399.
 A. Filipin, A. Jurasić, On the size of Diophantine mtuples for linear polynomials, Miskolc Mathematical Notes, 17 (2016), 2; 861876.
 C. Fuchs, A. Jurasić, R. Paulin, Elementary resolution of a family of quartic Thue equations over function fields, Monatsh. Math., 180 (2016), 2; 205211.

N. Grbac, H. Grobner, The residual Eisenstein cohomology of Sp_{4} over a totally real number field
Trans. Amer. Math. Soc. 365 (2013), no. 10, 51995235.  N. Grbac, F. Shahidi, Endoscopic transfer for unitary groups and holomorphy of Asai Lfunctions, Pacific J. Math. 276 (2015), no. 1, 185211.
 M. Kanovich, T. Ban Kirigin, V. Nigam, A. Scedrov, Bounded memory DolevYao adversaries in collaborative systems. Information and computation, Special issue on Security and Rewriting Techniques. 238 (2014) 233261.
 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) 332375.
 M. Kanovich, T. Ban Kirigin, V. Nigam, A. Scedrov, C. Talcott, Discrete vs. dense times in the analysis of cyberphysical security protocols, In: Proceedings of the 4th International Conference on Principles of Security and Trust (POST ‘15), Lecture Notes in Computer Science vol. 9036, pp. 259–279, SpringerVerlag, 2015.
 L. Rubin, V. Tonić, Simultaneous Z/pacyclic resolutions of expanding sequences, Glasnik Matematički 48, (2013.) 443466.