Division of Algebra and Number Theory

Chair:
 

  • Assoc. Prof. Ana Jurasić



Members:

  • Prof. Predrag Dominis Prester
  • Assoc. Prof. Tajana Ban Kirigin
  • Assoc. Prof. Marijana Butorac
  • Assoc. Prof. Ana Jurasić
  • Assist. Prof. Sanda Bujačić Babić
  • Assist. Prof. Vera Tonić
  • Dr. 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. The Division has 8 members, five of which are holding tenure track positions, one senior teaching assistant, 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).

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, čiji su voditelji dr. sc. Hrvoje Buljan i dr. sc. Pavle Pandžić.


Active research projects in which members of the Division participate:
 



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 2013-2017
  • 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 2014-2018
  • Algebraic and Combinatorial Methods in Vertex Algebra Theory (principal investigator: Dražen Adamović), Croatian Science Foundation research grant no. 2634 for the period 2014-2018
  • Diophantine m-tuples, Elliptic Curves, Thue and Index Form Equations (principal investigator: Andrej Dujella), Croatian Science Foundation research grant no. 6422 for the period 2014-2018
  • Regulated Collaborative Systems: Foundations and Applications (principal investigator: V. Nigam), Research Without Borders project (Brazil) for the period 2013-2016
  • Cyber Protocols in the Physical Environment (principal investigator: A. Scedrov), Office of Naval Research (ONR), USA, for the period 2015-2018
  • Complex Language Networks- LangNet (principal investigator: Sanda Martinčić-Ipšić), University of Rijeka initial research grant no.13.13.2.2.07 for the period 2014-2017
  • Cohomology of Arithmetic Groups and Automorphic Forms (principal investigators: Neven Grbac and Joachim Schwermer), bilateral cooperation project  of Croatia and Austria for the period 2014-2015
  • Foundations of geometric approximate group theory (principal investigator: Tobias Hantrick) , project based on the KIT Karlsruhe University in Germany during 2018
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Selection of research papers:
 

 
  • A. Filipin, A. Jurasić, A polynomial variant of a problem of Diophantus and its consequences, Glasnik matematički, 54 (2019), 1; 21-52.
  • 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.
  • S. Bujačić, A variation of a congruence of Subbarao for n=2α5β, α, β≥0, Periodica Mathematica Hungarica 75 (1), 66 – 79, 2017.
  • M. Butorac, C. Sadowski, Combinatorial bases of principal subspaces of modules for twisted affine Lie algebras of type A2l-1, Dl(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.
  • A. Filipin, A. Jurasić, On the size of Diophantine m-tuples for linear polynomials, Miskolc Mathematical Notes, 17 (2016), 2; 861-876.
  • 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.
  • 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, C. Talcott, Time, Computational Complexity, and Probability in the Analysis of Distance-Bounding Protocols, Journal of Computer Security, 25(6): 585-630, 2017.
  • A. A. Urquiza, M. A. Alturki, M- Kanovich, T. Ban Kirigin, V. Nigam, A. Scedrov, C. Talcott, Resource-Bounded Intruders in Denial of Service Attacks, In 2019 IEEE 32nd Computer Security Foundations Symposium (CSF), IEEE Computer Society Press, pp.382-396, 2019.
  • L. Rubin, V. Tonić, Simultaneous Z/p-acyclic resolutions of expanding sequences, Glasnik Matematički 48, (2013.) 443-466.
 
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