Common valuations of division polynomials]//, with Matteo Verzobio, accepted at Proc. A. R. Soc. Edinb. Published online 2024:1-15.(open access) - //Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6//, with Julie Desjardins, accepted at Ann. Inst. Fourier ([[https://arxiv.org/abs/1911.02684|preprint+code) - 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) - Diophantine triples and K3 surfaces, with Matija Kazalicki, J. 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 Crystallogr., Sect. A: Found. Adv. (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 Crystallogr., Sect. A: Found. Adv. (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, Commun. Number Theory Phys. (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, J. Number Theory (2020), Vol. 213, 152-186. (preprint version) - The generalized Fermat equation with exponents 2, 3, n, with Nuno Freitas and Michael Stoll, Compos. Math., 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 Publ. 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 ===== - Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve, with Stefan Barańczuk and Matteo Verzobio, submitted (preprint) - Explicit equations of 800 conics on a Barth-Bauer quartic, submitted(preprint) - Second moments and the bias conjecture for the family of cubic pencils, with Matija Kazalicki, submitted (preprint+code) - On a certain hypergeometric motive of weight 2 and rank 3, submitted (preprint) - Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms, submitted (preprint) ===== 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