Published papers

  1. Mathematical discovery in the age of artificial intelligence, with Ken Ono, Nat. Phys.(2025), Vol. 21, 1504–1506
  2. Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve, with Stefan Barańczuk and Matteo Verzobio, J. Number Theory (2026), Vol. 279, 170-183. (open access)
  3. Second moments and the bias conjecture for the family of cubic pencils, with Matija Kazalicki, Math. Z.(2025) 309, 72. 1-31. (preprint+code)
  4. Periodic arrangements of closely packed spheres, with Zbigniew Dauter and Mariusz Jaskolski, ChemTexts (2025) 11, 2. 1-17. (open access)
  5. Growth functions of periodic space tessellations, with Jakub Malinowski, Zbigniew Dauter and Mariusz Jaskolski, Acta Crystallogr., Sect. A: Found. Adv. (2025), Vol. 81, No. 1, 64-81. (open access)
  6. Common valuations of division polynomials, with Matteo Verzobio, Proc. A. R. Soc. Edinb. (2025), Vol. 155, No. 5, 1646-1660.(open access)
  7. Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6, with Julie Desjardins, Ann. Inst. Fourier 74 (2024) No. 5, 2231-2274 (open access+code)
  8. The Euler characteristic as a basis for teaching topology concepts to crystallographers, with Zbigniew Dauter and Mariusz Jaskólski, J. Appl. Cryst., (2022), Vol. 55, 154-167. (open access)
  9. Diophantine triples and K3 surfaces, with Matija Kazalicki, J. Number Theory (2022), Vol. 236, 41-70 (open access)
  10. A topological proof of the modified Euler characteristic based on the orbifold concept, with Zbigniew Dauter and Mariusz Jaskólski, Acta Crystallogr., Sect. A: Found. Adv. (2021), Vol.7, No. 4, 317-326. (open access)
  11. Arithmetic proof of the multiplicity-weighted Euler characteristic for symmetrically arranged space-filling polyhedra, with Zbigniew Dauter and Mariusz Jaskólski, Acta Crystallogr., Sect. A: Found. Adv. (2021), Vol.7, No. 2, 126-129. (open access)
  12. Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell-Yan scattering, with Marco Besier, Dino Festi and Michael Harrison, Commun. Number Theory Phys. (2020), Vol. 14, No. 4, 863-911. (open access)
  13. Primitive divisors of elliptic divisiblity sequences over function fields with constant j-invariant, with Marco Streng, J. Number Theory (2020), Vol. 213, 152-186. (open access)
  14. The generalized Fermat equation with exponents 2, 3, n, with Nuno Freitas and Michael Stoll, Compos. Math.(2020), Vol. 156 (1), 77-113. (see also a poster for STEM for Britain) (preprint version)
  15. On higher congruences between cusp forms and Eisenstein series II, Notes from the International Autumn School on Computational Number Theory: Izmir Institute of Technology 2017 (2019), Birkhäuser, (preprint version)
  16. Divisibility sequences of polynomials and heights estimates, New York J. Math. 22 (2016), 989-1020. (open access)
  17. Distribution of Mordell-Weil ranks of families of elliptic curves, Banach Center Publ.(2016) 108 , 201-229.(open access)
  18. On higher congruences between cusp forms and Eisenstein series in Computations with Modular Forms © Springer-Verlag (2014), Vol. 6, 257-277. (preprint version)
  19. Mordell–Weil ranks of families of elliptic curves associated to Pythagorean triples, Acta Arith.(2013) 160, 159-183. (open access)
  20. Infinite family of elliptic curves of rank at least 4, Involve (2010), Vol. 3, No. 3 , 297–316 (open access)

Preprints

  1. On the geography of log-surfaces, with Piotr Pokora, submitted (preprint)
  2. Explicit equations of 800 conics on a Barth-Bauer quartic, submitted(preprint)
  3. On a certain hypergeometric motive of weight 2 and rank 3, submitted (preprint)
  4. Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms, submitted (preprint)

Popular writing

In preparation

  1. Equiangular lines and an elliptic surface, with Dan Fretwell and Neil I. Gillespie, in preparation
  2. On realisations of weight 0 hypergeometric motives of small degrees, in preparation (with Magma package)

Theses

"Rangi w rodzinach krzywych eliptycznych i formy modularne", Ph. D. thesis, 2014

"O pewnym równaniu diofantycznym", M. Sc. thesis, 2010