Marija Bliznac Trebješanin
Faculty of Science, University of Split – 21000 Split – Croatia
H +385 (98) 977 8307 • B marbli@pmfst.hr
www.pmfst.hr/~marbli

Research Interests{ Diophantine equations– especially Diophantine m-tuples, i.e. sets with the property that theproduct of any two of its distinct elements is one less than a square.

Education
Department of Mathematics, Faculty of Science, University of Zagreb
PhD, Thesis: Diophantine D(4)-m-tuples and related problems (in Croatian)

2014-2018

Doctoral program in Mathematics. Supervisor : Professor dr. sc. Alan Filipin.

Faculty of Science, University of Split
Master’s degree

2012–2014

Graduate Studies in Mathematics, Computer Course

Faculty of Science, University of Split
Bachelor’s degree

2009–2012

Undergraduate Studies in Mathematics and Computer Science.

Work experience
Faculty of Science, University of Split
Assistant professor

April 2019-

Faculty of Science, University of Split
Research and teaching assistantMarch 2017-2019

Faculty of Civil Engineering, University of Zagreb
Research assistantFebruary 2015–March 2017

I am PhD student and a member of the Croatian Science Foundation project „Diophantine m-tuples, elliptic
curves, Thue and index form equations“.

Faculty of Science, University of Split
Teaching Assistant

October 2014.– February 2015.

I was a teaching assistant for undergraduate and graduate courses "Introduction to Number Theory", "Cryptography" and "Introduction to Analytic Geometry and Algebra".

Publications{ M. Bliznac, A. Filipin, An upper bound for the number of Diophantine quintuples, Bull. Aust.
Math. Soc., 94(3) (2016), 384–394., doi:10.1017/S0004972716000423{ M. Bliznac Trebješanin, A. Filipin, A. Jurasic, On the polynomial quadruples with the property
D(−1; 1), Tokyo J. Math. 41 (2018), 527-540. doi:10.3836/tjm/1502179250{ M. Bliznac Trebješanin, A. Filipin, Nonexistence of D(4)-quintuples, J. Number Theory 194(2019), 170-217 doi:10.1016/j.jnt.2018.07.013
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{ M. Bliznac Trebješanin, Extension of a Diophantine triple with the property D(4), Acta Math.
Hungar. 163 (2021), 213-246. doi:10.1007/s10474-020-01128-0{ M. Bliznac Trebješanin, D(4)-triples with two largest elements in common, Math. Slovaca, vol.
73, no. 2, (2023), 343-352.
{ K. N. Adédji, M. Bliznac Trebješanin, A. Filipin, A. Togbé, On the D(4)-pairs {a, ka} withk ∈ {2, 3, 6}, Glas. Mat. Ser. III 58 (2023), 35-57.
{ M. Bliznac Trebješanin, S. Bujačić, Polynomial D(4)-quadruples over Gaussian integers, Glas.
Mat. Ser. III 59 (2024), 1-31.
{ K. N. Adédji, M. Bliznac Trebješanin, On Mixed Concatenations of Pell and Pell-Lucas Numbers
which are Pell Numbers, Mathematica Pannonica 30 (2024), 91-104.
{ M. Bliznac Trebješanin, P. Radić, On extensions of D(4)-triples by adjoining smaller elements,Publicationes Mathematicae Debrecen, accepted for publication

Conference Talks and Posters{ Upper bound on number of D(4)-quintuples, poster presentation, 6th Croatian MathematicalCongress, Faculty of Science, University of Zagreb (July 2016.){ Nonexistence of D(4)-quintuples, short talk, 30th Journées Arithmétiques, University of Caen,France, (July 2017.){ Diophantine D(4)-m-tuples, poster presentation, 20th International Workshop for Young Mathematicians ”Number Theory”., Jagiellonian University, Krakow, Poland, (September 2017.){ Extensions of a D(4)-triple, short talk, Representation Theory XVI, Dubrovnik, Croatia, (June2019.){ The regularity of D(4)-m-tuples, poster presentation, 7th Croatian Mathematical Congress, Split,Croatia, (June 2022){ D(4)-triples with two largest elements in common, Conference on Diophantine m-tuples andrelated problems III, Zagreb, Croatia, (September 2022)

Other Talks{ The number of D(4)-quintuples, Seminar on Number Theory and Algebra, University of Zagreb.
(March 2016.){ There does not exist a D(4)-quintuple , Seminar on Number Theory and Algebra, University ofZagreb. (April 2017.)

Conferences and Workshops Attended{ Workshop on Number Theory and Algebra, University of Zagreb, Zagreb, Croatia, 11.2014.
{ Galois Theory and Number Theory, University of Konstanz, Konstanz, Germany, 7.2015.
{ 6th Croatian Mathematical Congress, University of Zagreb, Zagreb, Croatia 6.2016.
{ 30th Journées Arithmétiques, Caen, France, 7.2017.
{ Workshop for Young Mathematicians ”Number Theory”, Jagiellonian University, Krakow, Poland,
9.2017.
{ Torsion groups and Galois representations of elliptic curves, University of Zagreb, Zagreb, Croatia
6.2018.
{ Representation Theory XVI, Dubrovnik, Croatia, 6.2019.
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{ 7th Croatian Mathematical Congress, Split, Croatia, 7.2022.
{ Conference on Diophantine m-tuples and related problems III, 9.2022.

Scientific Research Experience
2023–“Number theory and arithmetic geometry”, Croatian Science
Fundation project, Grant no. IP-2022-10-5008, (Principal investigator: Filip Najman)
2018–2022 "Diophantine Geometry And Applications", Croatian Science
Fundation project, Grant no. IP-2018-01-1313, (Principal investigator: Matija Kazalicki)
2020–2022 "A contemporary approach to some classical Diophantine problems", joint austrian-croatian project,
2014–2018 "Diophantine m-tuples, elliptic curves, Thue and index formequations", Croatian Science Fundation project, Grant no. 6422,(Principal investigator: Andrej Dujella)
2016–2017 project " Classical Problems of Diophant, Fermat and Ritt using
New Analytic and Algebraic Techniques"- joint austrian-croatian
project

Relevant Skills
Languages:
Computer skills:

English, Croatian
LaTex, Wolfram Mathematica, C#, Python

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