Arthur Bik's Webpage

Personal picture of Arthur Bik

Contact Information

Max Planck Institute for Mathematics in the Sciences

Inselstraße 22

04103 Leipzig

Germany

Office: G3 01

I am a postdoctoral reseacher in the Nonlinear Algebra group of Bernd Sturmfels at the Max Planck Institute for Mathematics in the Sciences in Leipzig. Before, I was a PhD student at 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

Arthur Bik, Jan Draisma, Rob H. Eggermont and Andrew Snowden: The geometry of polynomial representations.
Arthur Bik, Alessandro Danelon and Jan Draisma: Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum.

Publications

Arthur Bik, Alessandro Danelon, Jan Draisma and Rob H. Eggermont: Universality of high-strength tensors, Vietnam J. Math. (2021). arXiv
Edoardo Ballico, Arthur Bik, Alessandro Oneto and Emanuele Ventura: Strength and slice rank of forms are generically equal, Israel J. Math. (2021), to appear. arXiv
Edoardo Ballico, Arthur Bik, Alessandro Oneto and Emanuele Ventura: The set of forms with bounded strength is not closed, Comptes Rendus Math. (2021), to appear. arXiv
Arthur Bik, Henrik Eisenmann and Bernd Sturmfels: Jordan Algebras of Symmetric Matrices, Le Matematiche 76 (2021), no 2, pp. 337-353. arXiv
Arthur Bik and Alessandro Oneto: On the strength of general polynomials, Linear Multilinear Algebra (2021). arXiv
Note: We verified the final claim in the article using SAGE and NumPy. See here for the used code.
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.
Arthur Bik, Jan Draisma, Alessandro Oneto and Emanuele Ventura: The monic rank, Math. Comput. 89 (2020), no. 325, pp. 2481–2505. arXiv
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.
Arthur Bik: Noetherianity up to conjugation of locally diagonal inverse limits, Linear Algebra Appl. 582 (2019), pp. 237–290. arXiv
Note: See this erratum.
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

You can download my PhD thesis here.
You can download my MSc thesis here.
You can download my BSc thesis here.

Award and Fellowship

SNSF Postdoc.Mobility Fellowship (24 months), 10 December 2020.
Diamant Award for the best talk by a PhD student, DIAMANT Symposium Fall 2017, Breukelen, 1 December 2017.

Talks

Strength of polynomials, TAPIRS Seminar, University of Michigan via Zoom, 29 October 2021.
Strength of polynomials via polynomial functors, SIAM Conference on Applied Algebraic Geometry, Texas A&M via Zoom, 20 August 2021.
Strength of Polynomials, Seminar on Nonlinear Algebra, MPI Leipzig, 13 August 2021.
Strength of Polynomials, Mathematical Colloquium, Bern via Zoom, 12 April 2021.
Jordan algebras of symmetric matrices, Applied Algebra and Analysis Online Seminar, Braunschweig/Osnabrück via Zoom, 15 January 2021.
Strength of polynomials via polynomial functors, Student/Postdoc Working Geometry Seminar, College Station via Zoom, 30 December 2020.
Polynomial functors as affine spaces, Nonlinear Algebra Seminar Online, Leipzig via Zoom, 28 April 2020.
Strength and polynomial functors, Seminar on Nonlinear Algebra, Leipzig, 22 January 2020.
Semi-algebraic properties of Minkowski sums of a twisted cubic segement, 9th swiss-french workshop in Algebraic Geometry, Charmey, 14 January 2020
Strength and polynomial functors, 20th Graduate Colloquium, Geneva, 19 November 2019.
Strength and polynomial functors, SIAM Conference on Applied Algebraic Geometry, Bern, 9 July 2019.
The monic rank and instances of Shapiro's Conjecture, MEGA 2019, Madrid, 20 June 2019.
Semi-algebraic properties of Minkowski sums of the bounded twisted cubic, SMS Doctoral Day 2019, Bern, 10 May 2019.
The monic rank and instances of Shapiro's Conjecture, Graduate Student Meeting on Applied Algebra and Combinatorics, Leipzig, 18 February 2019.
Polynomials of bounded strength, DIAMANT Symposium Fall 2018, Veenendaal, 29 November 2018.
Polynomials of bounded strength, Summer School on Graphical Models, Basel, 28 June 2018.
Noetherianity up to conjugation, Seminar Algebra and Geometry, Basel, 8 May 2018.
Noetherianity of dualized adjoint representations up to locally diagonal groups, DIAMANT Symposium Spring 2018, Veldhoven, 5 April 2018.
Euclidean distance degrees of orthogonally invariant varieties, DIAMANT Symposium Fall 2017, Breukelen, 30 November 2017.
Euclidean distance degrees of affine subvarieties of polar representations, InterCity - seminar, Fribourg, 6 October 2017.
ED Degrees of Orthogonally Invariant Varieties, SIAM Conference on Applied Algebraic Geometry, Atlanta, 4 August 2017.

Organized Events

Minisymposium Algebra and Geometry of Tensors 2: structured tensors, SIAM AG21, Texas A&M, 16-20 August 2021.
co-organized with Jan Draisma and Emanuele Ventura.

Assisted Courses

(Spring 2020) Mathematics for Data Science @ University of Bern
(Fall 2019) Algebra @ University of Bern
(Spring 2019) Algorithmen in der Algebra @ University of Bern
(Fall 2018) Galois Theory @ University of Bern
(Spring 2018) Analysis 2 @ University of Bern
(Fall 2017) Algebra: Gruppen und Körper @ University of Bern
(Spring 2017) Lineare Algebra 2 @ University of Bern
(Fall 2016) Lineare Algebra 1 @ University of Bern
(Spring 2016) Numerieke Methoden 1 @ Delft University of Technology
(Spring 2015) Numerieke Methoden 1 @ Delft University of Technology

Travels

SIAM Conference on Applied Algebraic Geometry, Zoom, 16 - 20 August 2021.
Tensor Networks: Quantum Physics, Geometry and Applications, Levico Terme, 26 - 28 July 2021.
GO 60: Pure & Applied Algebraic Geometry celebrating Giorgio Ottaviani’s 60th birthday, Zoom, 21 - 25 June 2021.
MEGA 2021: Effective Methods in Algebraic Geometry, Zoom, 7 - 11 June 2021.
Research visit MPI MiS Leipzig, Leipzig, 20 - 24 January 2020.
9th swiss-french workshop in Algebraic Geometry, Charmey, 13 - 17 January 2020.
DIAMANT Symposium Fall 2019, Utrecht, 28 - 29 November 2019.
20th Graduate Colloquium, Geneva, 18 - 20 November 2019.
TiME 2019: Curves and Surfaces, A History of Shapes, Levico Terme, 2 - 6 September 2019.
SIAM Conference on Applied Algebraic Geometry, Bern, 9 - 13 July 2019.
MEGA 2019: Effective Methods in Algebraic Geometry, Madrid, 17 - 21 June 2019.
Workshop on Applied Algebra, Braunschweig, 7 - 8 June 2019.
Graduate Student Meeting on Applied Algebra and Combinatorics, Leipzig, 18 - 20 February 2019.
Advances in Applied Algebraic Geometry, Bristol, 11 - 14 December 2018.
DIAMANT Symposium Fall 2018, Veenendaal, 29 - 30 November 2018.
Michigan Representation Stability Week 2018, Ann Arbor, 13 - 17 August 2018.
Summer School Graphical Models, Basel, 25 - 29 June 2018.
Weekend Course “Introduction to Algebraic Statistics”, Berlin, 25 - 27 May 2018.
DIAMANT Symposium Spring 2018, Veldhoven, 4 - 5 April 2018.
DIAMANT Symposium Fall 2017, Breukelen, 30 November - 1 December 2017.
Meeting on Matroids over Hyperfields, Fribourg, 28 - 29 August 2017.
SIAM Conference on Applied Algebraic Geometry, Atlanta, 31 July - 4 August 2017.
PhD Course: Quantum Information Theory and Geometry, Povo, 10 - 14 July 2017.
International Workshop on "Quantum Physics and Geometry", Levico Terme, 4 - 6 July 2017.
6th Swiss-French Workshop on Algebraic Geometry, Charmey, 9 - 13 January 2017.
Cremona Conference, Basel, 5 - 16 September 2016.