This is an old revision of the document!

Published papers

  1. Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell-Yan scattering, with Marco Besier, Dino Festi and Michael Harrison, accepted in Communications in Number Theory and Physics(preprint version+ code)
  2. Primitive divisors of elliptic divisiblity sequences over function fields with constant j-invariant, with Marco Streng, Journal of Number Theory (2020), 152-186 (preprint version)
  3. The generalized Fermat equation with exponents 2, 3, n, with Nuno Freitas and Michael Stoll (preprint version), Compositio Mathematica, Vol. 156 (1) (2020), 77-113. (see also a poster for STEM for Britain)
  4. 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)
  5. Divisibility sequences of polynomials and heights estimates, New York J. Math. 22 (2016), 989-1020. (preprint version)
  6. Distribution of Mordell-Weil ranks of families of elliptic curves, Banach Center Publications 108 (2016), 201-229,DOI: 10.4064/bc108-0-16 (preprint version)
  7. On higher congruences between cusp forms and Eisenstein series in Computations with Modular Forms © Springer-Verlag, Volume 6 (2014), 257-277 (preprint version)
  8. Mordell–Weil ranks of families of elliptic curves associated to Pythagorean triples, Acta Arith. 160 (2013), 159-183 ( preprint version)
  9. Infinite family of elliptic curves of rank at least 4, Involve, Vol. 3, No. 3 (2010), 297–316 ( preprint version)

Preprints

  1. Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6, with Julie Desjardins, submitted(preprint+code)
  2. On a certain hypergeometric motive of weight 2 and rank 3, submitted (preprint)
  3. Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms, submitted (preprint)

In preparation

  1. Bias conjecture for cubic pencils, with Matija Kazalicki, in preparation - Equiangular lines and an elliptic surface, with Dan Fretwell and Neil I. Gillespie, in preparation - Diophantine triples and K3 surfaces, with Matija Kazalicki, in preparation - 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