Publications

Preprints and journal articles

A list of my publications and preprints can be downloaded here (last updated: November 20, 2024):

DOWNLOAD publi...st-3.pdf

Selected preprints (see also arXiv)

Logarithmic Discriminants of Hyperplane Arrangements, with Leonie Kayser and Andreas Kretschmer
Proudfoot-Speyer Degenerations of Scattering Equations, with Barbara Betti and Viktoriia Borovik
Euler Stratifications of Hypersurface Families, with Maximilian Wiesmann
Santaló Geometry of Convex Polytopes, with Dmitrii Pavlov (accepted for publication in SIAM Journal of Applied Algebra and Geometry)
Adjoints and Canonical Forms of Tree Amplituhedra, with Kristian Ranestad and Rainer Sinn (accepted for publication in Mathematica Scandinavica)
Chebyshev Varieties, with Zaïneb Bel-Afia and Chiara Meroni
Hilbert Functions of Chopped Ideals, with Fulvio Gesmundo and Leonie Kayser. (accepted for publication in Journal of Algebra)
Tropical Implicitization Revisited, with Kemal Rose and Bernd Sturmfels.
Twisted Cohomology and Likelihood Ideals, with Saiei-Jaeyeong Matsubara-Heo.
The Algebraic Degree of Coupled Oscillators, with Paul Breiding, Mateusz Michalek and Leonid Monin.
Introduction to Toric Geometry
Adjoints and Canonical Forms of Polypols, with Kathlén Kohn, Ragni Piene, Kristian Ranestad, Felix Rydell, Boris Shapiro, Rainer Sinn, Miruna-Stefana Sorea. (accepted for publication in Documenta Mathematica)
Yet another Eigenvalue Algorithm for Solving Polynomial Systems, with Matías R. Bender.

Journal articles

Daniele Agostini, Claudia Fevola, Anna-Laura Sattelberger, and Simon Telen. "Vector spaces of generalized Euler integrals". In: Communications in Number Theory and Physics 18.2 (2024), pp. 327–370. DOI: 10.4310/CNTP.2024.v18.n2.a2
Claudia Fevola, Sebastian Mizera, and Simon Telen. "Principal Landau determinants". In: Computer Physics Communications 303 (2024), p. 109278. ISSN: 0010-4655. DOI: 10.1016/j.cpc.2024.109278
Barbara Betti, Marta Panizzut, and Simon Telen. "Solving equations using Khovanskii bases". In: Journal of Symbolic Computation 126 (2025), p. 102340. ISSN: 0747-7171. DOI: 10.1016/j.jsc.2024.102340
Claudia Fevola, Sebastian Mizera, and Simon Telen. "Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals". In: Phys. Rev. Lett. 132 (10 Mar. 2024), p. 101601. DOI: 10.1103/PhysRevLett.132.101601
Saiei-Jaeyeong Matsubara-Heo, Sebastian Mizera, and Simon Telen. "Four lectures on Euler integrals". In: SciPost Phys. Lect. Notes (2023), p. 75. DOI: 10.21468/SciPostPhysLectNotes.75
Rob Claes, Karl Meerbergen, and Simon Telen. "Contour Integration for Eigenvector Nonlinearities". In: SIAM Journal on Matrix Analysis and Applications 44.4 (2023), pp. 1619–1644. DOI: 10.1137/22M1497985
Dmitrii Pavlov, Bernd Sturmfels, and Simon Telen. "Gibbs manifolds". In: Information Geometry (2023). DOI: 10.1007/s41884-023-00111-2
Timothy Duff, Simon Telen, Elise Walker, and Thomas Yahl. "Polyhedral homotopies in Cox coordinates". In: Journal of Algebra and Its Applications (2023), p. 2450073. DOI: 10.1142/S0219498824500737
Bernd Sturmfels, Simon Telen, François-Xavier Vialard, and Max von Renesse. "Toric geometry of entropic regularization". In: Journal of Symbolic Computation 120 (2024), p. 102221. ISSN: 0747-7171. DOI: 10.1016/j.jsc.2023.102221
Daniele Agostini, Taylor Brysiewicz, Claudia Fevola, Lukas Kühne, Bernd Sturmfels, Simon Telen, and Thomas Lam. "Likelihood degenerations". In: Advances in Mathematics 414 (2023), p. 108863. ISSN: 0001-8708. DOI: 10.1016/j.aim.2023.108863
Michael Borinsky, Anna-Laura Sattelberger, Bernd Sturmfels, and Simon Telen. "Bayesian Integrals on Toric Varieties". In: SIAM Journal on Applied Algebra and Geometry 7.1 (2023), pp. 77–103. DOI: 10.1137/22M1490569
Simon Telen and Nick Vannieuwenhoven. "A Normal Form Algorithm for Tensor Rank Decomposition". In: ACM Trans. Math. Softw. 48.4 (Dec. 2022). ISSN: 0098-3500. DOI: 10.1145/3555369
Sebastian Mizera and Simon Telen. "Landau discriminants". In: Journal of High Energy Physics 2022.8 (2022), pp. 1–57. DOI: 10.1007/JHEP08(2022)200
Matías R. Bender and Simon Telen. "Toric eigenvalue methods for solving sparse polynomial systems". In: Mathematics of Computation 91.337 (2022), pp. 2397–2429. DOI: 10.1090/mcom/3744
Bernd Sturmfels and Simon Telen. "Likelihood equations and scattering amplitudes". In: Algebraic Statistics 12.2 (2021), pp. 167–186. DOI: 10.2140/astat.2021.12.167
Simon Telen, Marc Van Barel, and Jan Verschelde. "A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation". In: SIAM Journal on Scientific Computing 42.6 (2020), A3610–A3637. DOI: 10.1137/19M1288036
Simon Telen, Sascha Timme, and Marc Van Barel. "Backward error measures for roots of polynomials". In: Numerical Algorithms 87.1 (2021), pp. 19–39. DOI: 10.1007/s11075-020-00956-z
Simon Telen. "Numerical root finding via Cox rings". In: Journal of Pure and Applied Algebra 224.9 (2020), p. 106367. ISSN: 0022-4049. DOI: 10.1016/j.jpaa.2020.106367
Bernard Mourrain, Simon Telen, and Marc Van Barel. "Truncated normal forms for solving polynomial systems: Generalized and efficient algorithms". In: Journal of Symbolic Computation 102 (2021), pp. 63–85. ISSN: 0747-7171. DOI: 10.1016/j.jsc.2019.10.009
Simon Telen, Bernard Mourrain, and Marc Van Barel. "Solving Polynomial Systems via Truncated Normal Forms". In: SIAM Journal on Matrix Analysis and Applications 39.3 (2018), pp. 1421–1447. DOI: 10.1137/17M1162433
Simon Telen and Marc Van Barel. "A stabilized normal form algorithm for generic systems of polynomial equations". In: Journal of Computational and Applied Mathematics 342 (2018), pp. 119–132. ISSN: 0377-0427. DOI: 10.1016/j.cam.2018.04.021

Presentations (last updated: September 12, 2024)

Primer on semidefinite programming, August 2024, kick-off meeting for the ERC project UNIVERSE+, Bad Honnef
Discriminants in the sciences, June 2024, Meeting of the Scientific Advisory Board, MPI MiS
Chebyshev varieties, June 2024, Mathematics of Data Science, MPI MiS Leipzig
Chebyshev varieties, May 2024, Back to the Roots seminar, KU Leuven
Introduction to positive geometry, May 2024, Positive Solutions of Polynomial Systems Arising from Real-life Application, University of Granada
Euler discriminants in physics and statistics, New Frontiers in Landau Analysis, The Higgs Centre for Theoretical Physics, Edinburgh
Euler discriminants in physics and statistics, Methusalem colloquium, KU Leuven
Santaló geometry of convex polytopes, January 2024, workshop on applied and computational algebraic geometry, ISAAC Newton Institute for mathematical sciences, Cambridge
Computational algebraic geometry for Landau analysis, January 2024, Motives and period integrals in quantum field theory and string theory, University of Oxford
Tensors, polynomials and applications, November 2023, Chemnitz Mathematical Colloquium, TU Chemnitz
Twisted cohomology and likelihood ideals, November 2023, Forschungsseminar Algebra und Theoretische Mathematik, TU Chemnitz
Tensors, polynomials and applications, November 2023, Tensor day, Università degli studi di Trento
Chebyshev varieties, October 2023, Seminar Algebra-Geometrie-Kombinatorik, TU Dresden
Principal Landau Determinants, October 2023, Tropical geometry and infrared divergences, IAS Princeton
Principal Landau Determinants, September 2023, MathemAmplitudes, Universitá di Padova
Chebyshev varieties, September 2023, Workshop on Computational and Applied Mathematics, on the occasion of Marc Van Barel's retirement, Selva di Fasano
Twisted cohomology and likelihood ideals, August 2023, ICIAM, Waseda University, Tokyo
Structured root finding via eigenvalues: beyond toric varieties, August 2023, workshop on hypergeometric functions, Kobe University
Structured root finding via eigenvalues: beyond toric varieties, July 2023, SIAM Conference on Applied Algebraic Geometry, TU Eindhoven
Hilbert functions in computational algebraic geometry, May 2023, Research Seminar Algebra, Friedrich-Schiller Universität, Jena
Toric varieties and Gibbs manifolds in convex optimization, May 2023, Algebraic statistics seminar, Max Planck Institute for Mathematics in the Sciences, Leipzig
Hilbert functions in computational algebraic geometry, April 2023, Dresden-Leipzig seminar Algebra and Geometry, University of Leipzig
Toric varieties and Gibbs manifolds in convex optimization, March 2023, MATHEXP-PolSys seminar, Sorbonne Université, Paris
Twisted cohomology and likelihood ideals, February 2023, guest lecture in Melody Chan's group meeting, Brown University
Twisted cohomology and likelihood ideals, February 2023, Amplitudes Group Meeting, IAS Princeton
Toric varieties and Gibbs manifolds in convex optimization, February 2023, Applied CATS seminar (online), KTH Stockholm
Amplituhedra of lines in three-space, January 2023, Mini-Workshop on Positive Geometry, TU Munich
Vector spaces of generalized Euler integrals, January 2023, Joint Mathematics Meetings, Boston
Numerical nonlinear algebra in particle physics, November 2022, DIAMANT symposium, Leiden
Complexity of tensor decomposition and Hilbert functions, November 2022, AGATES Algebraic Geometry and Complexity Theory, IMPAN, Warsaw
Toric geometry of entropic regularization, November 2022, Oberseminar Algebra, Osnabrück
Toric geometry of entropic regularization, October 2022, N&O seminar, CWI Amsterdam
Solving polynomial equations and applications, October 2022, Workshop on Solving Polynomial Equations and Applications, CWI Amsterdam
Generalized Euler integrals: (co)homology and tropical numerics, September 2022, ETH ITS Zürich
Toric geometry of entropic regularization, July 2022, CTU Prague
Toric geometry of entropic regularization, June 2022, MEGA 22 conference, Krakow
Toric geometry of entropic regularization, May 2022, applied analysis seminar, MPI MiS Leipzig
Landau discriminants, April 2022, Nonlinear algebra and combinatorics from physics, Harvard, Boston
Bayesian integrals on toric varieties, April 2022, Mini-workshop on algebraic statistics, Harvard, Boston
Landau discriminants, April 2022, ETH ITS Zürich
Tropical integration in physics and statistics, April 2022, MPI MiS Leipzig
Discriminants from particle physics, April 2022, Nonlinear algebra day, RWTH Aachen
Numerical nonlinear algebra in particle physics, February 2022, Nonlinear algebra seminar online
Likelihood equations and scattering amplitudes, February 2022, UC Riverside Algebraic Geometry Seminar (online)
Toric techniques for solving sparse polynomial equations, February 2022, KU Leuven, Leuven
Polyhedral homotopies in Cox coordinates, January 2022, RSME, Ciudad Real
Landau Discriminants, November 2021, IAS Princeton
Adjoints and Canonical Forms of Polypols, September 2021, Nonlinear Algebra Seminar, MPI MiS Leipzig
A normal form method for numerical tensor rank decomposition, August 2021, SIAM Conference on Applied Algebraic Geometry, Texas A&M (online)
Likelihood Equations and Positive Geometries, July 2021, Math of Data workshop, MPI MiS Leipzig
A normal form method for numerical tensor rank decomposition, May 2021, Applied Algebra and Analysis Online Seminar
Likelihood Equations and Scattering Amplitudes, May 2021, Seminar Diskrete Mathematik & Diskrete Geometrie
Likelihood Equations and Scattering Amplitudes, April 2021, HEP seminars at Southampton
Eigenvalue methods for solving polynomial systems, March 2021, N&O Seminar, CWI, Amsterdam
Likelihood Equations and Scattering Amplitudes, March 2021, Algebraic Statistics Online Seminar
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
Robust Numerical Path Tracking in Polynomial Homotopies, July 2019, ICIAM conference, Valencia
Solving nonlinear eigenvalue problems using contour integration, July 2019, ICIAM conference, Valencia
Numerical Root Finding via Cox Rings, July 2019, SIAM AG19, Bern
Robust Numerical Path Tracking in Polynomial Homotopies, April 2019, NUMA seminar, Department of Computer Science, KU Leuven
Stabilized Algebraic Methods for Multivariate Polynomial Root Finding, March 2019, CIIRC Prague
Stabilized Algebraic Methods for Multivariate Polynomial Root Finding, December 2018, MPI MiS Leipzig
Structured Matrices in Polynomial System Solving, May 2018, SIAM Conference on Applied Linear Algebra (SIAM-ALA18), Hong Kong
Polynomial System Solving through Stabilized Representation of Quotient Algebras, April 2018, BYU, Provo
Polynomial System Solving and Numerical Linear Algebra, July 2017, SIAM AG17, Georgia Tech, Atlanta
Matrices in polynomial system solving, May 2017, Rencontre en Algèbre Linéaire Numérique Amiens-Calais, Amiens
Systems of Polynomial Equations and Numerical Linear Algebra, May 2017, NUMA seminar, KU Leuven
Solving Systems of Polynomial Equations, July 2016, International Linear Algebra Society (ILAS) conference, Leuven

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:

DOWNLOAD thesis.pdf