Arthur Bik's Webpage

I was a Postdoc.Mobility fellow at the University of Neuchâtel in the research group of Elisa Gorla from August 2023 to January 2024. Before that I was a postdoctoral member at the Institute for Advanced Study in Princeton for the 2022-2023 academic year and participant in the Special-Year Program on Dynamics, Additive Number Theory and Algebraic Geometry. I was a postdoctoral researcher at the Nonlinear Algebra group of Bernd Sturmfels at the Max Planck Institute for Mathematics in the Sciences in Leipzig, partly as a Postdoc.Mobility fellow. I obtained my PhD from the University of Bern supervised by Jan Draisma, I obtained my MSc from Leiden University supervised by Ronald van Luijk and Roland van der Veen and I obtained my BSc from Delft University of Technology supervised by Ronald van Luijk.

Preprints

  1. Arthur Bik, Jan Draisma, Andrew Snowden: Two improvements in Brauer's theorem on forms.
  2. Arthur Bik, Jan Draisma, Rob Eggermont, Andrew Snowden: Uniformity for limits of tensors.
  3. Arthur Bik, Alessandro Neri: Higher-degree symmetric rank-metric codes.
  4. Arthur Bik, Alessandro Danelon, Andrew Snowden: Isogeny classes of cubic spaces.
  5. Arthur Bik and Orlando Marigliano: Classifying one-dimensional discrete models with maximum likelihood degree one.
       Note: The code used for the computations in Sections 6, 7 and 8 is on MathRepo.

Publications

  1. Arthur Bik and Henrik Eisenmann: The Geometries of Jordan nets and Jordan webs, Ann. di Mat. Pura ed Appl. 201 (2022), pp 2413–2464. arXiv
       Note: The code used for the computations in Section 5 is on MathRepo.
  2. Arthur Bik, Jan Draisma, Rob H. Eggermont and Andrew Snowden: The geometry of polynomial representations, Int. Math. Res. Not. (2022). arXiv
  3. Arthur Bik, Alessandro Danelon, Jan Draisma and Rob H. Eggermont: Universality of high-strength tensors, Vietnam J. Math. 50 (2022), pp. 557–580. arXiv
  4. Edoardo Ballico, Arthur Bik, Alessandro Oneto and Emanuele Ventura: Strength and slice rank of forms are generically equal, Israel J. Math. 254 (2023), pp. 275–291. arXiv
  5. Edoardo Ballico, Arthur Bik, Alessandro Oneto and Emanuele Ventura: The set of forms with bounded strength is not closed, Compt. Rend. Math. 360 (2022), pp. 371–380. arXiv
  6. Arthur Bik, Alessandro Danelon and Jan Draisma: Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum, Math. Ann. 385 (2023), pp. 1879–1921. arXiv
  7. Arthur Bik, Henrik Eisenmann and Bernd Sturmfels: Jordan Algebras of Symmetric Matrices, Le Matematiche 76 (2021), no 2, pp. 337–353. arXiv
       Note: See here for code used in computations in the paper.
  8. Arthur Bik and Alessandro Oneto: On the strength of general polynomials, Linear Multilinear Algebra 70 (2022), no. 21, pp. 6114–6140. arXiv
       Note: We verified the final claim in the article using SAGE and NumPy. See here for the used code.
  9. Arthur Bik, Adam Czapliński and Markus Wageringel: Semi-algebraic properties of Minkowski sums of a twisted cubic segment, Collect. Math. 72 (2021), no. 1, pp. 87–107. arXiv
       Note: You can find models of some of these sets here.
  10. Arthur Bik, Jan Draisma, Alessandro Oneto and Emanuele Ventura: The monic rank, Math. Comput. 89 (2020), no. 325, pp. 2481–2505. arXiv
  11. Arthur Bik, Jan Draisma and Rob H. Eggermont: Polynomials and tensors of bounded strength, Commun. Contemp. Math. 21 (2019), no. 7, 1850062 (24 pages). arXiv
       Note: See these errata.
  12. Arthur Bik: Noetherianity up to conjugation of locally diagonal inverse limits, Linear Algebra Appl. 582 (2019), pp. 237–290. arXiv
       Note: See this erratum.
  13. Arthur Bik and Jan Draisma: A note on ED degrees of group-stable subvarieties in polar representations, Israel J. Math. 228 (2018), no. 1, pp. 353–377. arXiv

Theses

Awards and Fellowship

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