Published papers

  1. Diophantine triples and K3 surfaces, with Matija Kazalicki, Journal of Number Theory (2021, in press) (open access)
  2. A topological proof of the modified Euler characteristic based on the orbifold concept, with Zbigniew Dauter and Mariusz Jaskólski, Acta Crystallographica Section A: Foundations and Advances (2021), Vol.7, No. 4, 317-326 (open access)
  3. Arithmetic proof of the multiplicity-weighted Euler characteristic for symmetrically arranged space-filling polyhedra, with Zbigniew Dauter and Mariusz Jaskólski, Acta Crystallographica Section A: Foundations and Advances (2021), Vol.7, No. 2, 126-129 (open access)
  4. Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell-Yan scattering, with Marco Besier, Dino Festi and Michael Harrison, Communications in Number Theory and Physics (2020), Vol. 14, No. 4, 863-911(preprint version+ code)
  5. Primitive divisors of elliptic divisiblity sequences over function fields with constant j-invariant, with Marco Streng, Journal of Number Theory (2020), Vol.213, 152-186 (preprint version)
  6. The generalized Fermat equation with exponents 2, 3, n, with Nuno Freitas and Michael Stoll, Compositio Mathematica, Vol. 156 (1) (2020), 77-113. (see also a poster for STEM for Britain) (preprint version)
  7. 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, Birkhäuser, 2019 (preprint version)
  8. Divisibility sequences of polynomials and heights estimates, New York J. Math. 22 (2016), 989-1020. (preprint version)
  9. Distribution of Mordell-Weil ranks of families of elliptic curves, Banach Center Publications 108 (2016), 201-229,(preprint version)
  10. On higher congruences between cusp forms and Eisenstein series in Computations with Modular Forms © Springer-Verlag, Volume 6 (2014), 257-277 (preprint version)
  11. Mordell–Weil ranks of families of elliptic curves associated to Pythagorean triples, Acta Arith. 160 (2013), 159-183 ( preprint version)
  12. Infinite family of elliptic curves of rank at least 4, Involve, Vol. 3, No. 3 (2010), 297–316 ( preprint version)

Preprints

  1. Explicit equations of 800 conics on a Barth-Bauer quartic, (preprint)
  2. Second moments and the bias conjecture for the family of cubic pencils, with Matija Kazalicki, submitted (preprint+code)
  3. Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6, with Julie Desjardins, submitted(preprint+code)
  4. On a certain hypergeometric motive of weight 2 and rank 3, submitted (preprint)
  5. Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms, submitted (preprint)

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