Publications

Journal articles

  • Telen S., Van Barel M., Verschelde J. (2020). A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation. SIAM Journal on Scientific Computing, 42 (6), A3610-A3637.

  • Telen S., Timme S. and Van Barel M (2020). Backward error measures for roots of polynomials. Numerical Algorithms: 1-21.
  • Telen S. (2020). Numerical Root Finding via Cox Rings. Journal of Pure and Applied Algebra, 224(9), 2020.
  • Mourrain B., Telen S., Van Barel M. (2021). Truncated Normal Forms for Solving Polynomial Systems: Generalized and Efficient Algorithms. Journal of Symbolic Computation, 102, 63-85. 

  • Telen S., Mourrain B., Van Barel M. (2018). Solving Polynomial Systems Via Truncated Normal Forms. SIAM Journal on Matrix Analysis and Applications, 39 (3), 1421-1447. doi: 10.1137/17M1162433.
  • Telen S., Van Barel M. (2018). A Stabilized Normal Form Algorithm for Generic Systems of Polynomial Equations. Journal of Computational and Applied Mathematics, 342, 119-132.

Presentations

  • Likelihood Equations and Scattering Amplitudes, February 2021, Geomplitudes, online meeting organized by UC Davis.
  • Cox homotopies: tracking homogeneous coordinates on toric varieties, January 2021, Joint Mathematics Meetings,
  • Polyhedral Homotopies in Cox Coordinates, November 2020, Nonlinear Algebra Seminar Online.
  • Solving Polynomial Systems via Truncated Normal Forms, October 2020, NumPi Seminar, Pisa.

  • Numerical Root Finding via Cox Rings, February 2020, Milestone conference of the thematic Einstein semester `Algebraic Geometry', Berlin.
  • Numerical Root Finding via Cox Rings, January 2020, Forschungsseminar Diskrete Mathematik/Geometrie, TU Berlin.
  • Truncated Normal Forms, December 2019, Algorithmic Algebra Seminar, TU Berlin.
  • Numerical Root Finding via Cox Rings, November 2019, Seminar Algebraische Geometrie, FU Berlin.
  • Telen S., Van Barel M., Verschelde J. , Robust Numerical Path Tracking in Polynomial Homotopies. Presented at the ICIAM conference, Valencia, 19 Jul 2019.
  • Van Barel M., Telen S., Solving nonlinear eigenvalue problems using contour integration. Presented at the ICIAM conference, Valencia, 15 Jul 2019.
  • Telen S., Numerical Root Finding via Cox Rings. Presented at the SIAM AG conference, Bern, 12 Jul 2019.
  • Telen S., Van Barel M., Verschelde J. , Robust Numerical Path Tracking in Polynomial Homotopies. Presented at the NUMA seminar, Department of Computer Science, KU Leuven, 3 Apr 2019.
  • Telen S., Van Barel M., Mourrain B., Stabilized Algebraic Methods for Multivariate Polynomial Root Finding. Presented during a research visit to CIIRC Prague 5 Mar 2019.
  • Telen S., Van Barel M., Mourrain B., Stabilized Algebraic Methods for Multivariate Polynomial Root Finding. Presented during a research visit to MPI Leipzig, 11 Dec 2018.
  • Telen S., Van Barel M., Structured Matrices in Polynomial System Solving. Presented at the SIAM Conference on Applied Linear Algebra (SIAM-ALA18), 4-8 May 2018.
  • Telen S., Mourrain B., Van Barel M., Polynomial System Solving through Stabilized Representation of Quotient Algebras. Presented during a research visit to BYU, Provo, 3 Apr 2018.
  • Telen S., Van Barel M., Polynomial System Solving and Numerical Linear Algebra. Presented at the SIAM Conference on Applied Algebraic Geometry, Georgia Institute of Technology, Atlanta, Georgia, USA, 31 Jul 2017-04 Aug 2017.
  • Telen S., Van Barel M., Matrices in polynomial system solving. Presented at the RENcontre en Algèbre Linéaire Numérique Amiens-CAlais, Amiens, France, 30 May 2017.
  • Telen S., Van Barel M., Systems of Polynomial Equations and Numerical Linear Algebra. Presented at the NUMA seminar, KU Leuven, Belgium, 18 May 2017-18 May 2017.
  • Telen S., Van Barel M., Solving Systems of Polynomial Equations. Presented at the Conference of the International Linear Algebra Society, Leuven, Belgium, 11 Jul 2016-15 Jul 2016.

Posters

  • Telen S., Numerical Root Finding via Cox Rings. Presented at the opening conference of the thematic Einstein semester `Algebraic Geometry' at FU Berlin, Oct 2019.
  • Telen S., Van Barel M., Verschelde J., Robust Numerical Path Tracking for Polynomial Homotopies. Presented at the 2019 MEGA conference in Madrid, 17-21 Jun 2019.
  • Telen S., Numerical Root Finding via Cox Rings. Presented at the conference `Ideals, Varieties and Applications' (celebrating the influence of David Cox), Jun 2019.
  • Telen S., Mourrain B., Van Barel M., Truncated Normal Forms for Solving Polynomial Systems. Presented at the ICERM nonlinear algebra semester, Sep 2018.
  • Telen S., Mourrain B., Van Barel M., Truncated Normal Forms for Solving Polynomial Systems. Presented at the ISSAC 2018 conference in New York, 16-19 Jul 2018.
  • Telen S., Mourrain B., Van Barel M., Truncated Normal Forms for Solving Polynomial Systems. Presented at the 2018 CBMS conference on Applications of Polynomial Systems at TCU, Texas, 4-8 Jun 2018.

Master's Thesis

I wrote my master's thesis under the supervision of my PhD advisor Marc Van Barel. It is entitled `Solving Systems of Polynomial Equations' and can be found here.

PhD Thesis

I wrote my PhD thesis under the supervision of Marc Van Barel. It is entitled 'Solving Systems of Polynomial Equations'. Take a look: