1 Einstein Drive

Princeton

NJ 08540

USA

Office: Fuld-412

E-mail: mabik@ias.edu

Institute for Advanced Study

1 Einstein Drive

Princeton

NJ 08540

USA

Office: Fuld-412

E-mail: mabik@ias.edu

I am 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. Before, 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. Before that, 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.

- Arthur Bik, Jan Draisma, Rob Eggermont, Andrew Snowden: Uniformity for limits of tensors.
- Arthur Bik, Alessandro Neri: Higher-degree symmetric rank-metric codes.
- Arthur Bik, Alessandro Danelon, Andrew Snowden: Isogeny classes of cubic spaces.
- 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.

- 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. - Arthur Bik, Jan Draisma, Rob H. Eggermont and Andrew Snowden: The geometry of polynomial representations, Int. Math. Res. Not. (2022). arXiv
- Arthur Bik, Alessandro Danelon, Jan Draisma and Rob H. Eggermont: Universality of high-strength tensors, Vietnam J. Math. 50 (2022), pp. 557–580. arXiv
- 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
- 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
- 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
- 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. - 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. - 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

- Mathematical Institute Prize for Outstanding PhD Thesis, 21 December 2021.
- SNSF Postdoc.Mobility Fellowship (24 months), 10 December 2020.
- Diamant Award for the best talk by a PhD student, DIAMANT Symposium Fall 2017, 1 December 2017.

- Strength of infinite Polynomials, Seminar, University of Michigan via Zoom, 6 April 2023.
- Strength of infinite Polynomials, Geometry Seminar, Texas A&M, 20 March 2023.
- One-parameter subgroups, stability and Kempf's theorem, Special Year seminar, Institute for Advanced Study, 7 December 2022.
- Strength of (infinite) Polynomials, Applied Algebra Seminar, University of Wisconsin-Madison, 20 October 2022.
- Strength of Polynomials, Short Talks by Postdoctoral Members, Institute for Advanced Study, 20 September 2022.
- Curves with a rational MLE and chipfiring games, Seminar on Nonlinear Algebra, MPI Leipzig, 23 March 2022.
- 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, University of 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, MPI Leipzig via Zoom, 28 April 2020.
- Strength and polynomial functors, Seminar on Nonlinear Algebra, MPI 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.

- Minisymposium Asymptotic Algebra and Geometry, SIAM AG23, TU Eindhoven, 10-14 July 2023.

co-organized with Rob Eggermont and Aida Maraj. - 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.

- (Summer 2022) Representation theory of finite groups @ University of Leipzig

- (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

- SIAM Conference on Applied Algebraic Geometry, Eindhoven, 10 - 14 July 2023.
- Combinatorial, Computational, and Applied Algebraic Geometry, Seattle, 27 June - 1 July 2022.
- Workshop on geometry and complexity theory, Toulouse, 25 - 29 April 2022.
- 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.