algebra

Algebra > BI > FSE > RUG

Publications (since 2017)

2023

  1. A K3 surface related to Leonardo Pisano’s work on congruent numbers ( and ), In Expos. Math., . [doi]
  2. The CM class number one problem for curves of genus 2 ( and ), In Res. Number Theory, volume 9, . [url] [doi]
  3. Quadratic Chabauty for modular curves: algorithms and examples (, , , and ), In Compos. Math., volume 159, . [url] [doi]
  4. Computing torsion subgroups of Jacobians of hyperelliptic curves of genus 3 ( and ), In Res. Number Theory, volume 9, . [url] [doi]
  5. On initials and the fundamental theorem of tropical partial differential algebraic geometry (, , , , and ), In J. Symbolic Comput., volume 115, . [url] [doi]

2022

  1. A remark on prime (non)congruent numbers (, and ), In Quaest. Math., volume 45, . [url] [doi]
  2. A parametrized set of explicit elements of Sha$(E/\Bbb Q)[3]$ ( and ), In Integers, volume 22, .
  3. In memoriam Bas Edixhoven (1962–2022): generous, optimistic and committed (, , and ), In Nieuw Arch. Wiskd. (5), volume 23, .
  4. Rational points on del Pezzo surfaces of degree four ( and ), In Int. J. Number Theory, volume 18, . [url] [doi]
  5. Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4 ( and ), In J. Number Theory, volume 236, . [url] [doi]
  6. Rank jumps on elliptic surfaces and the Hilbert property ( and ), In Ann. Inst. Fourier (Grenoble), volume 72, . [url] [doi]
  7. The expansion $\star\bmod\overline o(\hslash^4)$ and computer-assisted proof schemes in the Kontsevich deformation quantization ( and ), In Exp. Math., volume 31, . [url] [doi]
  8. The density of polynomials of degree $n$ over $\Bbb Z_p$ having exactly $r$ roots in $\Bbb Q_p$ (, , and ), In Proc. Lond. Math. Soc. (3), volume 124, . [url] [doi]
  9. $p$-adic integration on bad reduction hyperelliptic curves ( and ), In Int. Math. Res. Not. IMRN, . [url] [doi]
  10. Explicit Vologodsky integration for hyperelliptic curves (), In Math. Comp., volume 91, . [url] [doi]
  11. Autonomous first order differential equations (, and ), In Trans. Amer. Math. Soc., volume 375, . [url] [doi]

2021

  1. The last chapter of the Disquisitiones of Gauss (, and ), In Hardy-Ramanujan J., volume 44, .
  2. Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces (, , , and ), Chapter in Women in numbers Europe III—research directions in number theory, Springer, Cham, volume 24, . [url] [doi]
  3. Reduction types of genus-3 curves in a special stratum of their moduli space (, , , , and ), Chapter in Women in numbers Europe III—research directions in number theory, Springer, Cham, volume 24, . [url] [doi]
  4. The Kontsevich graph orientation morphism revisited ( and ), Chapter in Homotopy algebras, deformation theory and quantization, Polish Acad. Sci. Inst. Math., Warsaw, volume 123, . [url] [doi]
  5. Curves with sharp Chabauty-Coleman bound (), Chapter in Arithmetic geometry, number theory, and computation, Springer, Cham, . [url] [doi]
  6. Locally recoverable codes on surfaces (, and ), In IEEE Trans. Inform. Theory, volume 67, . [url] [doi]
  7. Two recent $p$-adic approaches towards the (effective) Mordell conjecture (, , , , , and ), Chapter in Arithmetic L-functions and differential geometric methods, Birkhäuser/Springer, Cham, volume 338, .
  8. Explicit quadratic Chabauty over number fields (, , and ), In Israel J. Math., volume 243, . [url] [doi]
  9. Serre's genus fifty example (), Chapter in Arithmetic, geometry, cryptography and coding theory, Amer. Math. Soc., [Providence], RI, volume 770, . [url] [doi]
  10. Two-descent on some genus two curves (, and ), In Indag. Math. (N.S.), volume 32, . [url] [doi]
  11. Mazur's rational torsion result for pointless genus one curves: examples (, and ), In Res. Number Theory, volume 7, . [url] [doi]

2020

  1. ${\rm Q}(\sqrt {-3})$-integral points on a Mordell curve (), Chapter in Mathematical software—ICMS 2020, Springer, Cham, volume 12097, . [url] [doi]
  2. The fundamental theorem of tropical partial differential algebraic geometry (, , , and ), In ISSAC'20—Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, ACM, New York, . [url] [doi]
  3. The minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheaf ( and ), In Kyoto J. Math., volume 60, . [url] [doi]
  4. Explicit arithmetic intersection theory and computation of Néron-Tate heights (, and ), In Math. Comp., volume 89, . [url] [doi]
  5. The level of pairs of polynomials (, and ), In Comm. Algebra, volume 48, . [url] [doi]
  6. A proof of the Hasse-Weil inequality for genus 2 it à la Manin ( and ), In Indian J. Pure Appl. Math., volume 51, . [url] [doi]
  7. Linear differential equations with finite differential Galois group (, and ), In J. Algebra, volume 553, . [url] [doi]
  8. Quadratic Chabauty for (bi)elliptic curves and Kim's conjecture (), In Algebra Number Theory, volume 14, . [url] [doi]
  9. A bound on the primes of bad reduction for CM curves of genus 3 (, , , , and ), In Proc. Amer. Math. Soc., volume 148, . [url] [doi]
  10. Primes dividing invariants of CM Picard curves (, and ), In Canad. J. Math., volume 72, . [url] [doi]
  11. A faithful 2-dimensional TQFT (, and ), In Homology Homotopy Appl., volume 22, . [url] [doi]

2019

  1. Chabauty-Coleman experiments for genus 3 hyperelliptic curves (, , , and ), Chapter in Research directions in number theory—Women in Numbers IV, Springer, Cham, volume 19, . [url] [doi]
  2. Archimedean local height differences on elliptic curves ( and ), In Acta Arith., volume 190, . [url] [doi]
  3. Explicit Chabauty-Kim for the split Cartan modular curve of level 13 (, , , and ), In Ann. of Math. (2), volume 189, . [url] [doi]
  4. Variations for some Painlevé equations (, and ), In SIGMA Symmetry Integrability Geom. Methods Appl., volume 15, . [url] [doi]
  5. Models illustrating a classification of plane cubic curves ( and ), In Math. Semesterber., volume 66, . [url] [doi]
  6. On certain maximal hyperelliptic curves related to Chebyshev polynomials ( and ), In J. Number Theory, volume 203, . [url] [doi]
  7. On the (non)removability of spectral parameters in $\Bbb Z_2$-graded zero-curvature representations and its applications ( and ), In Acta Appl. Math., volume 160, . [url] [doi]
  8. Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment (, and ), Chapter in Nonlinear systems and their remarkable mathematical structures. Vol. 1, CRC Press, Boca Raton, FL, .
  9. Modular invariants for genus 3 hyperelliptic curves (, , , , , and ), In Res. Number Theory, volume 5, . [url] [doi]
  10. Stratified bundles on curves and differential Galois groups in positive characteristic (), In SIGMA Symmetry Integrability Geom. Methods Appl., volume 15, . [url] [doi]
  11. Mumford curves and Mumford groups in positive characteristic ( and ), In J. Algebra, volume 517, . [url] [doi]

2018

  1. Rational Poncelet (, and ), In Int. J. Number Theory, volume 14, . [url] [doi]
  2. Hesse pencils and 3-torsion structures (, and ), In SIGMA Symmetry Integrability Geom. Methods Appl., volume 14, . [url] [doi]
  3. Counting points on the Fricke-Macbeath curve over finite fields ( and ), In J. Théor. Nombres Bordeaux, volume 30, . [url]
  4. The calculus of multivectors on noncommutative jet spaces (), In J. Geom. Phys., volume 130, . [url] [doi]
  5. Rational families of 17-torsion points of elliptic curves over number fields (, and ), Chapter in Number theory related to modular curves—Momose memorial volume, Amer. Math. Soc., Providence, RI, volume 701, . [url] [doi]

2017

  1. Computing integral points on hyperelliptic curves using quadratic Chabauty (, and ), In Math. Comp., volume 86, . [url] [doi]
  2. Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces ( and ), In Trans. Amer. Math. Soc., volume 369, . [url] [doi]
  3. Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication (, , , , , and ), Chapter in Algebraic geometry for coding theory and cryptography, Springer, Cham, volume 9, . [url] [doi]
  4. Albime triangles over quadratic fields ( and ), In Rocky Mountain J. Math., volume 47, . [url] [doi]
  5. Twists of elliptic curves (, and ), In SIGMA Symmetry Integrability Geom. Methods Appl., volume 13, . [url] [doi]
  6. Further remarks on rational albime triangles (, and ), In C. R. Math. Acad. Sci. Soc. R. Can., volume 39, .
  7. Isomonodromy for the degenerate fifth Painlevé equation (, and ), In SIGMA Symmetry Integrability Geom. Methods Appl., volume 13, . [url] [doi]
  8. The deformation quantisation mapping of Poisson to associative structures in field theory (), Chapter in 50th Seminar "Sophus Lie", Polish Acad. Sci. Inst. Math., Warsaw, volume 113, .
  9. The heptagon-wheel cocycle in the Kontsevich graph complex (, and ), In J. Nonlinear Math. Phys., volume 24, . [url] [doi]
  10. The Kontsevich tetrahedral flow revisited (, and ), In J. Geom. Phys., volume 119, . [url] [doi]