Division of Algebra and Number Theory

Chair:

Assist. Prof. Ana Jurasić


Members:

  • Assoc. Prof. Neven Grbac
  • Assist. Prof. Tajana Ban Kirigin
  • Assist. Prof. Marijana Butorac
  • Assist. Prof. Ana Jurasić
  • Assist. Prof. Vera Tonić
  • Sen. Lecturer Rene Sušanj
  • Dr. Sanda Bujačić
  • Dr. Nevena Jurčević Peček
  • Luka Mikec
     

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 9 members, five of which are holding tenure track positions, two senior teaching assistants, one teaching assistant and a senior lecturer.

Science

Scientific activities 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
  • Cohomology of arithmetic groups
  • Affine Lie algebras and vertex operator algebras
  • Diophantine and Thue equations
  • Dimension theories, Bockstein base, resolution theorems
  • Geometric group theory, coarse geometry
  • The theory of computation, 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:
 

  • 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
  • Regulated Colaborative Systems: Foundations and Applications (principal investigator: Vivek Nigam)
    Research Without Borders project (Brazil) for the period 2013-2016
  • LangNet - Complex Language Networks (principal investigator: Sanda Martinčić-Ipšić)
    University of Rijeka initial research grant no. 13.13.2.2.07  for the period 2013-2015



Finished research projects in which members of the Division participated:

  • Unitary Representations of Classical Groups and Automorphic Forms (principal investigator: Marko Tadic)
    Croatian Ministry of Science, Education and Sport research project no. 037-0372794-2804 for the period 2007-2013
  • Vertex Operator Algebras and Infinite-dimensional Lie Algebras (principal investigator: Mirko Primc)
    Croatian Ministry of Science, Education and sports research project no. 037-0372794-2806 for the period 2007-2013
  • Diophantine Equations and Elliptic Curves (principal investigator: Andrej Dujella)
    Croatian Ministry of Science, Education and Sport research project no. 037-0372781-2821 for a period 2007-2013
  • Mathematical Logic and Applications (principal investigator: Zvonimir Šikić)
    Croatian Ministry of Science, Education and Sport research project no. 120-1203164-3074 period 2007-2013
  • Logic and Reality (principal investigator: Majda Trobok)
    Croatian Ministry of Science, Education and Sport research project no. 009-0091328-0941 for the period 2007-2013
  • Arithmetic-combinatorial Problems and Applications (principal investigator: Andrej Dujella)
    bilateral cooperation project of Croatia and Austria for the period 2010-2011


Selection of scientific articles:
 

  • N. Grbac, J. Schwermer
    On residual cohomology classes attached to relative rank one Eisenstein series for the symplectic group,
    Int. Math. Res. Not. IMRN 2011, no. 7, 1654-1705.
  • N. Grbac, H. Grobner
    The residual Eisenstein cohomology of  Sp4 over a totally real number field,
    Trans. Amer. Math. Soc. 365 (2013), no. 10, 5199-5235.
  • N. Grbac
    On the residual spectrum of split classical groups supported in the Siegel maximal parabolic subgroup
    Monatsh. Math. 163 (2011), no. 3, 301-314.
  • M. Butorac
    Combinatorial bases of principal subspaces for the affine Lie algebra of Type B2(1) ,
    J. Pure Appl. Agebra 218 (2014), no. 3, 424-447.
  • A. Dujella A. Jurasić
    On the size of sets in a polynomial variant of a problem of Diophantus
    Int. J. Number Theory 6 (2010), no.7, 1449-1471.
  • V. Tonić
    Bockstein basis and resolution theorems in extension theory
    Topology and its Appl. 157 (2010), 674-691.
  • M. Kanovich, T. Ban Kirigin, V. Nigam, A. Scedrov
    Bounded memory Dolev-Yao adversaries in collaborative systems
    In: Formal Aspects of Security and Trust (FAST 2010), pp. 18-33
    Lecture Notes in Computer Science vol. 6561, Springer-Verlag, 2011.
  • M. Kanovich, T. Ban Kirigin, V. Nigam, A. Scedrov
    Bounded memory protocols and progressing collaborative systems
    In: J. Crampton, S. Jajodia and K. Mayesthe (ed.): 18th European Symposium on Research in Computer Security (ESORICS 2013), pp. 309-326
    Lecture Notes in Computer Science vol. 8134, Springer-Verlag, 2013.