Number theory and arithmetic geometry

 

  Project information
Research project no. HRZZ IP-2022-10-5008 funded by the Croatian Science Foundation (HRZZ)
Hosting organization: Faculty of Science (PMF), University of Zagreb
Project duration: 48 months (from December 31, 2023 to December 30, 2027)
Total amount of funding: 166022.97 EUR
 
  Project summary
The project coordinates and supports the research activities of the Croatian number theory and arithmetic geometry group. Research topics are: Arithmetic of modular curves, Diophantine D(n)-m-tuples, Diophantine approximations, Application of deep learning in number theory and Congruences for sporadic sequences and modular forms.
 
  Principal investigator
  • Filip Najman, professor, Department of Mathematics, Faculty of Science, University of Zagreb
  Team members
  • Nikola Adžaga, assistant professor, Faculty of Civil Engineering, University of Zagreb
  • Alen Andrašek, PhD student, Faculty of Civil Engineering, University of Zagreb
  • Marija Bliznac Trebješanin, assistant professor, Department of Mathematics, Faculty of Science, University of Split
  • Sanda Bujačić Babić, assistant professor, Faculty of Mathematics, University of Rijeka
  • Maarten Derickx, postdoc, Faculty of Science, University of Zagreb
  • Goran Dražić , postdoc, Faculty of Food Techology and Biotechonlogy, University of Zagreb
  • Andrej Dujella, professor, Faculty of Science, University of Zagreb
  • Alan Filipin, professor, Faculty of Civil Engineering, University of Zagreb
  • Zrinka Franušić, associate professor, Department of Mathematics, Faculty of Science, University of Zagreb
  • Mirela Jukić Bokun, associate professor, School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek
  • Ana Jurasić, assistant professor, Faculty of Mathematics, University of Rijeka, Croatia
  • Matija Kazalicki, professor, Department of Mathematics, Faculty of Science, University of Zagreb
  • Ivan Novak, PhD student, Department of Mathematics, Faculty of Science, University of Zagreb
  • Lukas Novak, PhD student, Department of Mathematics, Faculty of Science, University of Zagreb
  • Petar Orlić, PhD student, Department of Mathematics, Faculty of Science, University of Zagreb
  • Tomislav Pejković, assistant professor, Department of Mathematics, Faculty of Science, University of Zagreb
  • Pavao Radić, PhD student, Department of Mathematics, Faculty of Science, University of Split
  • Ivan Soldo, associate professor, School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek
  Research publications

  In the 1st project year

[1] F. Najman, On r-isogenies over Q(\zeta_r) of elliptic curves with rational j-invariants, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 118 (2024), 134.
[2] B. S. Banwait, F. Najman, O. Padurariu, Cyclic isogenies of elliptic curves over a fixed quadratic field, Math. Comp. 93 (2024), 841-862.
[3] N. Freitas, F. Najman, Two results on x^r+y^r=dz^p , Proc. Amer. Math. Soc. 152 (2024), 591-598.
[4] N. Adžaga, T. Keller, P. Michaud-Jacobs, F. Najman, E. Ozman, B. Vukorepa, Computing quadratic points on modular curves X_0(N), Math. Comp. 93 (2024), 1371-1397.
[5] F. Najman, P. Orlić, Gonality of the modular curve X_0(N), Math. Comp. 93 (2024), 863-886.
[6] M. Jukić Bokun, I. Soldo, Extensions of D(-1)-pairs in some imaginary quadratic fields, New York Journal of Mathematics 30 (2024), 745-755.
[7] Z. Franušić, A. Jurasić, On nonexistence of D(n)-quadruples, Math. Slovaca 74 (2024), 835-844.
[8] M. Derickx, P. Orlić, Modular curves X0(N) with infinitely many quartic points, Res. Number Theory 10, article number 42, (2024)
[9] Z. Bujanović, M. Kazalicki, L. Novak, Murmurations of Mestre-Nagao sums, IJDSMS 02 (2024), 51-61.

  Doctoral dissertations

 

  Conference and seminar talks

  In the 1st project year

  • F. Najman, Q-curves, sporadic points, and Serre's uniformity conjecture, (invited confernece talk), 31.1.2024, 2024 Workshop on Number Theory and Algebra, Daejeon, South Korea
  • F. Najman, Quadratic points on modular curves, (invited confernece talk), 1.2.2024, 2024 Workshop on Number Theory and Algebra, Daejeon, South Korea
  • P. Orlić, Tetragonal modular quotients X^+_0(N), (confernece talk), 1.2.2024, 2024 Workshop on Number Theory and Algebra, Daejeon, South Korea
  • F. Najman, Elliptic curves, (invited confernece talk), 4.2.2024, 2024 Algebra Camp, Yangpyeong, South Korea
  • P. Orlić, Gonality of the modular curve X_0(N), (invited confernece talk), 4.2.2024, 2024 Algebra Camp, Yangpyeong, South Korea
  • F. Najman, Modular Curves, (invited confernece talk), 5.2.2024, 2024 Algebra Camp, Yangpyeong, South Korea
  • M. Kazalicki, Ranks of elliptic curves and deep neural networks, (invited conference talk), 27.2.2024, Hybrid Conference on AI-MATH, Rio de Janeiro, Brazil
  • M. Kazalicki, Ranks of elliptic curves and neural networks, (invited conference talk), 13.4.2024, Alpe - Adria seminar, Zagreb, Croatia
  • N. Adžaga, Low Degree Points on Modular Curves and Their Quotients, (confernece talk), 18.4.2024, The eighth mini symposium of the Roman Number Theroy Association, Rome, Italy
  • F. Najman, Hyperelliptic and trigonal modular curves, (confernece talk), 18.4.2024, The eighth mini symposium of the Roman Number Theroy Association, Rome, Italy
  • A. Filipin, On the extension of D(4)-triples {q,b,c}, (conference talk), 13.6.2024, Canadian Number Theory Association XVI (CNTA XVI), Toronto, Canada
  • A. Dujella High-rank elliptic curves with given torsion group, (invited conference talk), 25.6.2024, The Quest for the Hidden Simplicity of Noncommutative Harmonic Analysis and Representation Theory - a conference celebrating the 70th birthday of Marko Tadic, Zagreb, Croatia
  • Zrinka Franušić On polynomial D(n)-quadruples in Z[X], (conference talk), 2.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • Ana Jurasić, On the existence of D(2X+1)-quadruples in Z[X], (conference talk), 2.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • S. Bujačić Babić Polynomial D(4)-quadruples in R[X] , (conference talk), 3.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • A. Dujella Rational Diophantine sextuples with strong pair, (conference talk), 3.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • M. Jukić Bokun, The extendibility of parametric D(-1)-triples, (conference talk), 3.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • M. Kazalicki, Ranks of elliptic curves and deep neural networks, (invited conference talk), 3.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • F. Najman, Low degree points on modular curves, (plenary talk), 3.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • I. Novak, Degrees of cyclic isogenies of elliptic curves with rational j-invariant, (conference talk), 3.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • L. Novak, Quadratic twists of genus one curves, (conference talk), 3.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • I. Soldo, Diophantine m- tuples in certain imaginary quadratic rings, (conference talk), 3.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • P. Radić, New results on D(4)-m-tuples, (poster), 4.7.2024, 8th Croatian Mathematical Congress, Osijek, Croatia
  • M. Kazalicki, Improving Mestre-Nagao heuristics with data science, (invited conference talk), 13.11.2024, Murmurations in Arithmetic Geometry and Related Topics, Stony Brook, NY, USA
  Participation in summer schools, workshops, and conferences

  In the 1st project year

  • P. Orlic, A Modern Introduction to Number Theory, 1-6.9.2024, Pisa, Italy
  • I. Novak, A Modern Introduction to Number Theory, 1-6.9.2024, Pisa, Italy
  • P. Orlic, Introduction to Number Theory and Algebraic Curves, 9-20.9.2024, Belgrade, Serbia
  • I. Novak, Introduction to Number Theory and Algebraic Curves, 9-20.9.2024, Belgrade, Serbia
  • A. Andrašek, Introduction to Number Theory and Algebraic Curves, 4-8.11.2024, Groningen, Netherlands
  Organization of workshops

  In the 1st project year

  Open positions

  Postdoc position 1 year, start date April or May 2024: Maarten Derickx joins us.

  Announcements
  December 31, 2023 Project started.