Mirela Jukić Bokun

MJB Assistant Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸
phone: +385-31-224-842
fax: +385-31-224-801
email:  mirela @ mathos.hr
office:  15 (ground floor)

 


Research Interests

Number Theory (Elliptic Curves, Diophantine Equations)

Degrees

PhD in Mathematics, Department of Mathematics, University of Zagreb, 2011.
MSc in Mathematics, Department of Mathematics, University of Zagreb, Croatia, 2008.
BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2001. 

Publications

Journal Publications

  1. A. Dujella, M. Jukić Bokun, I. Soldo, On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields, RACSAM (2016), prihvaćen za objavljivanje
    The possible torsion groups of elliptic curves induced by Diophan- tine triples over quadratic fields, which do not appear over Q, are Z/2Z × Z/10Z, Z/2Z × Z/12Z and Z/4Z × Z/4Z. In this paper, we show that all these torsion groups indeed appear over some quadratic field. Moreover, we prove that there are infinitely many Diophantine triples over quadratic fields which induce elliptic curves with these tor- sion groups.
  2. J. Aguirre, A. Dujella, M. Jukić Bokun, J.C. Peral, High rank elliptic curves with prescribed torsion group over quadratic fields, Periodica Mathematica Hungarica 68 (2014), 222-230
    There are 26 possibilities for the torsion group of elliptic curves defined over quadratic number fields. We present examples of high rank elliptic curves with given torsion group which give the current records for most of the torsion groups. In particular, we show that for each possible torsion group, except maybe for Z/15Z, there exist an elliptic curve over some quadratic field with this torsion group and with rank >= 2.
  3. M. Jukić Bokun, Elliptic curves over quadratic fields with fixed torsion subgroup and positive rank, Glasnik Matematički 47 (2012), 277-284
    For each of the torsion groups Z/2ZxZ/10Z, Z/2ZxZ/12Z, Z/15Z we find the quadratic field with the smallest absolute value of its discriminant such that there exists an elliptic curve with that torsion and positive rank. For the torsion groups Z/11Z, Z/14Z we solve the analogous problem after assuming the Parity conjecture.
  4. M. Jukić Bokun, On the rank of elliptic curves over Q(sqrt{-3}) with torsion groups Z/3Z x Z/3Z and Z/3Z x Z/6Z, Proceedings of the Japan Academy. Series A Mathematical sciences 87/5 (2011), 61-64
    We construct elliptic curves over the field Q(sqrt{-3}) with torsion group Z/3Z x Z/3Z and ranks equal to 7 and an elliptic curve over the same field with torsion group Z/3Z x Z/6Z and rank equal to 6.
  5. A. Dujella, M. Jukić Bokun, On the rank of elliptic curves over Q(i) with torsion group Z/4Z × Z/4Z, Proceedings of the Japan Academy. Series A Mathematical sciences 86/6 (2010), 93-96
    We construct an elliptic curve over Q(i) with torsion group Z/4Z * Z/4Z and rank equal to 7 and a family of elliptic curves with the same torsion group and rank >= 2.


Others

  1. M. Đumić, M. Jukić Bokun, Euklidov algoritam, Osječki matematički list 13 (2013), 121-137
  2. M. Duk, M. Jukić Bokun, L'Hospitalovo pravilo, Poučak 51 (2012), 19-31
  3. M. Jukić, Apolonijev problem, Osječki matematički list 2/2 (2002), 81-90
  4. M. Jukić, Broj e, Osječki matematički list 1/2 (2001), 79-85



Projects

  • Diophantine m-tuples, elliptic curves, Thue and index form equations 

Project leader: prof. dr. Andrej Dujella, Department of Mathematics, University of Zagreb. Project was funded in 2014 by the Croatian Science Foundation

  • Passive control of mechanical models

Project leader: prof. dr. Ninoslav Truhar, Deptartment of Mathematics, University of Osijek. Scientific project No.235-2352818-1042 of the Croatian Ministry of Science, Education and Sports for period 2007.-2013. (junior researcher)

  • Statistical aspects of parameter identification problems

Project leader: prof. dr. Mirta Benšić, Deptartment of Mathematics, University of Osijek. Scientific project No. 0235002 of the Croatian Ministry of Science, Education and Sports for period 2002.-2006. (junior researcher)

 


 

Professional Activities

Editorial Boards
  • Since 2012. technical editor of the international journal Mathematical Communications

Committee Memberships

Refereeing/Reviewing

 Refereeing:

  • Osječki matematički list 

Workshops and Conferences

with talk:

  • Elliptic curves over quadratic fields with fixed torsion subgroup and positive rank, 5th Croatian Mathematical Congress, Rijeka, Croatia, June 18 - 21, 2012
  • High rank elliptic curves with prescribed torsion group over quadratic fields, Workshop on Number Theory and Algebra, Department of Mathematics, University of Zagreb, Zagreb, Croatia, November 26-28, 2014
  • On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields,1st Croatian Combinatorial Days, Zagreb, Croatia, September 29-30, 2016
  • On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields,XXXth Journées Arithmétiques, Caen, France, July 3-7, 2017 

without talk:

  • Winter School on Explicit Methods in Number Theory, Debrecen, Hungary, January 26-30, 2009 

Seminar Talks 

Service Activities


Teaching

 

Konzultacije (Office Hours): Po dogovoru.

Prijedlog tema za diplomske i završne radove  

Diplomski i završni radovi 

Nastava u akademskoj godini 2016./2017.

Financijska i aktuarska matematika 

Metodika nastave matematike II

Uvod u teoriju brojeva

Matematika (Poljoprivredni fakultet, stručni studij)

Nastavne aktivnosti u prošlosti (Past Courses)

Analitička geometrija, Algebra Integralni račun Obične diferencijalne jednadžbe, Geometrija prostora i ravnine, Elementarna matematika I, Elementarna matematika II, Linearna algebra I, Linearna algebra II, Linearna algebra III  (Odjel za matematiku)

Matematika (Ekonomski fakultet) 

Matematika III, Matematička analiza II, Linearna algebra (Elektrotehnički fakultet)


Personal