Published papers
- The Euler characteristic as a basis for teaching topology concepts to crystallographers, with Zbigniew Dauter and Mariusz Jaskólski, Journal of Applied Crystallography, (2022), Vol. 55, 154-167. (open access)
- Diophantine triples and K3 surfaces, with Matija Kazalicki, Journal of Number Theory (2022), Vol. 236, 41-70 (open access)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- Divisibility sequences of polynomials and heights estimates, New York J. Math. 22 (2016), 989-1020. (preprint version)
- Distribution of Mordell-Weil ranks of families of elliptic curves, Banach Center Publications 108 (2016), 201-229.(preprint version)
- On higher congruences between cusp forms and Eisenstein series in Computations with Modular Forms © Springer-Verlag, Volume 6 (2014), 257-277. (preprint version)
- Mordell–Weil ranks of families of elliptic curves associated to Pythagorean triples, Acta Arith. 160 (2013), 159-183. ( preprint version)
- Infinite family of elliptic curves of rank at least 4, Involve, Vol. 3, No. 3 (2010), 297–316 ( preprint version)
Preprints
In preparation
- Equiangular lines and an elliptic surface, with Dan Fretwell and Neil I. Gillespie, 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