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| ===== Published papers ===== | ===== Published papers ===== | ||
| - | - //[[https://doi.org/10.1016/j.jnt.2021.07.009|Diophantine triples and K3 surfaces]]//, with Matija Kazalicki, Journal of Number Theory (2021, in press) (open access) | + | - [[https://doi.org/10.1016/j.jnt.2025.06.001 | 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) |
| - | - //[[https://doi.org/10.1107/S2053273321004320 | 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) | + | - //[[https://rdcu.be/edbEv|Second moments and the bias conjecture for the family of cubic pencils]]//, with Matija Kazalicki, Math. Z. 309, 72 (2025). 1-31. ([[https://arxiv.org/abs/2012.11306|preprint]]+[[https://bnaskrecki.faculty.wmi.amu.edu.pl/doku.php/second_moments|code]]) |
| - | - //[[https://doi.org/10.1107/S2053273320016186 | 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) | + | - //[[https://doi.org/10.1007/s40828-024-00199-8|Periodic arrangements of closely packed spheres]]//, with Zbigniew Dauter and Mariusz Jaskolski, ChemTexts 11, 2 (2025). 1-17. (open access) |
| - | - //[[https://dx.doi.org/10.4310/CNTP.2020.v14.n4.a4|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([[https://arxiv.org/abs/1908.01079|preprint version]]+ [[drell_yan_k3s|code]]) | + | - //[[https://doi.org/10.1107/S2053273324010763|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) |
| - | - //[[https://doi.org/10.1016/j.jnt.2019.12.002|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 ([[https://arxiv.org/abs/1904.12393|preprint version]]) | + | - //[[https://doi.org/10.1017/prm.2024.7|Common valuations of division polynomials]]//, with Matteo Verzobio, Proc. A. R. Soc. Edinb. Published online (2024):1-15.(open access) |
| - | - //[[https://doi.org/10.1112/S0010437X19007693|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 [[http://www.setforbritain.org.uk/2017psr/M-NASKRECKI-3706-PSR.pdf| poster]] for [[http://www.setforbritain.org.uk/index.asp | STEM for Britain]]) ([[https://arxiv.org/abs/1703.05058|preprint version]]) | + | - //[[https://aif.centre-mersenne.org/item/10.5802/aif.3635.pdf|Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6]]//, with Julie Desjardins, Ann. Inst. Fourier 74 (2024) no.5 p. 2231-2274 (open access+[[https://zenodo.org/records/10659434|code]]) |
| + | - //[[https://doi.org/10.1107/s160057672101205x | 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) | ||
| + | - //[[https://doi.org/10.1016/j.jnt.2021.07.009|Diophantine triples and K3 surfaces]]//, with Matija Kazalicki, J. Number Theory (2022), Vol. 236, 41-70 (open access) | ||
| + | - //[[https://doi.org/10.1107/S2053273321004320 | 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) | ||
| + | - //[[https://doi.org/10.1107/S2053273320016186 | 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) | ||
| + | - //[[https://dx.doi.org/10.4310/CNTP.2020.v14.n4.a4|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) | ||
| + | - //[[https://doi.org/10.1016/j.jnt.2019.12.002|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) | ||
| + | - //[[https://doi.org/10.1112/S0010437X19007693|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 [[http://www.setforbritain.org.uk/2017psr/M-NASKRECKI-3706-PSR.pdf| poster]] for [[http://www.setforbritain.org.uk/index.asp | STEM for Britain]]) ([[https://arxiv.org/abs/1703.05058|preprint version]]) | ||
| - //[[https://doi.org/10.1007/978-3-030-12558-5_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 ([[http://arxiv.org/abs/1810.02134|preprint version]]) | - //[[https://doi.org/10.1007/978-3-030-12558-5_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 ([[http://arxiv.org/abs/1810.02134|preprint version]]) | ||
| - | - //[[http://nyjm.albany.edu/j/2016/22-46.html|Divisibility sequences of polynomials and heights estimates]]//, New York J. Math. 22 (2016), 989-1020. ([[http://arxiv.org/abs/1609.04750|preprint version]]) | + | - //[[http://nyjm.albany.edu/j/2016/22-46.html|Divisibility sequences of polynomials and heights estimates]]//, New York J. Math. 22 (2016), 989-1020. (open access) |
| - | - //[[https://doi.org/10.4064/bc108-0-16|Distribution of Mordell-Weil ranks of families of elliptic curves]]//, Banach Center Publications 108 (2016), 201-229,([[http://arxiv.org/abs/1609.04731|preprint version]]) | + | - //[[https://doi.org/10.4064/bc108-0-16|Distribution of Mordell-Weil ranks of families of elliptic curves]]//, Banach Center Publ. 108 (2016), 201-229.(open access) |
| - | - //[[https://doi.org/10.1007/978-3-319-03847-6_10| On higher congruences between cusp forms and Eisenstein series]]// in Computations with Modular Forms © Springer-Verlag, Volume 6 (2014), 257-277 ([[http://arxiv.org/abs/1206.1881|preprint version]]) | + | - //[[https://doi.org/10.1007/978-3-319-03847-6_10| On higher congruences between cusp forms and Eisenstein series]]// in Computations with Modular Forms © Springer-Verlag, Volume 6 (2014), 257-277. ([[http://arxiv.org/abs/1206.1881|preprint version]]) |
| - | - //[[https://doi.org/10.4064/aa160-2-5 |Mordell–Weil ranks of families of elliptic curves associated to Pythagorean triples]]//, Acta Arith. 160 (2013), 159-183 ([[http://arxiv.org/abs/1210.6933| preprint version]]) | + | - //[[https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/160/2/83309/mordell-8211-weil-ranks-of-families-of-elliptic-curves-associated-to-pythagorean-triples |Mordell–Weil ranks of families of elliptic curves associated to Pythagorean triples]]//, Acta Arith. 160 (2013), 159-183. (open access) |
| - | - //[[https://doi.org/10.2140/involve.2010.3.297|Infinite family of elliptic curves of rank at least 4]]//, Involve, Vol. 3, No. 3 (2010), 297–316 ([[http://arxiv.org/abs/0909.3424| preprint version]]) | + | - //[[https://doi.org/10.2140/involve.2010.3.297|Infinite family of elliptic curves of rank at least 4]]//, Involve, Vol. 3, No. 3 (2010), 297–316 (open access) |
| ===== Preprints ===== | ===== Preprints ===== | ||
| - | - //Explicit equations of 800 conics on a Barth-Bauer quartic//, ([[https://arxiv.org/abs/2108.13402 |preprint]]) | + | - //On the geography of log-surfaces//, with Piotr Pokora, submitted ([[https://arxiv.org/abs/2412.14635|preprint]]) |
| - | - //Second moments and the bias conjecture for the family of cubic pencils//, with Matija Kazalicki, submitted ([[https://arxiv.org/abs/2012.11306|preprint]]+[[https://bnaskrecki.faculty.wmi.amu.edu.pl/doku.php/second_moments|code]]) | + | - //Explicit equations of 800 conics on a Barth-Bauer quartic//, submitted([[https://arxiv.org/abs/2108.13402 |preprint]]) |
| - | - //Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6//, with Julie Desjardins, submitted([[https://arxiv.org/abs/1911.02684|preprint]]+[[https://bnaskrecki.faculty.wmi.amu.edu.pl/doku.php/geometry_of_del_pezzo|code]]) | + | |
| - //{{:hyper24111.pdf|On a certain hypergeometric motive of weight 2 and rank 3}}//, submitted ([[https://arxiv.org/abs/1702.07738|preprint]]) | - //{{:hyper24111.pdf|On a certain hypergeometric motive of weight 2 and rank 3}}//, submitted ([[https://arxiv.org/abs/1702.07738|preprint]]) | ||
| - //Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms//, submitted ([[http://arxiv.org/abs/1609.04715|preprint]]) | - //Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms//, submitted ([[http://arxiv.org/abs/1609.04715|preprint]]) | ||
| + | |||
| + | ===== Popular writing ==== | ||
| + | * [[https://academia.pan.pl/czym-jest-szyfrowanie/|Czym jest szyfrowanie? (ACADEMIA (2023) No. 4 (76) pp. 18-21) ]] | ||
| + | * [[https://www.deltami.edu.pl/2024/05/jej-wysokosc-krzywa-eliptyczna/| Jej wysokość krzywa eliptyczna (Delta (2024) No. 5 (600) pp. 16-19)]] | ||
| + | |||
| ===== In preparation ===== | ===== In preparation ===== | ||
| - //Equiangular lines and an elliptic surface//, with Dan Fretwell and Neil I. Gillespie, in preparation | - //Equiangular lines and an elliptic surface//, with Dan Fretwell and Neil I. Gillespie, in preparation | ||