Sascha Timme

I was a PhD student at TU Berlin under the supervision of Michael Joswig and Bernd Sturmfels. I graduated in summer 2021. My main field of interest is Numerical Nonlinear Algebra, a subject at the intersection of Numerical Analysis and Algebraic Geometry. Together with Paul Breiding I am developing the Julia package HomotopyContinuation.jl, a package to solve systems of polynomial equations by numerical homotopy continuation methods.

I was supported by the Research Training Group Facets of Complexity and the Einstein Fellowship research group Nonlinear Algebra of Bernd Sturmfels.

Prior to my PhD I was a software engineer at the start-up Math 42 which was successfully aquired by Chegg in October 2017.

Interests. Nonlinear Algebra, Polynomial System Solving, Julia, Numerical Computations

Publications

Published

• Catastrophe in Elastic Tensegrity Frameworks (2021, with Alex Heaton), accepted for publication in Arnold Mathematical Journal.
• Mixed Precision Path Tracking for Polynomial Homotopy Continuation (2021), Advances in Computational Mathematics volume 47, Article number: 75
• Estimating linear covariance models with numerical nonlinear algebra (2020 with Bernd Sturmfels and Piotr Zwiernik, arXiv:1909.00566). Algebraic Statistics 11-1 (2020), 31--52.
• 96120: The degree of the linear orbit of a cubic surface (2019 with Laura Brustenga and Madeleine Weinstein). Le Matematiche 75 (2), 425-437.
• Polymake.jl: A new interface to polymake (2020 with Marek Kaluba and Benjamin Lorenz). Mathematical Software – ICMS 2020. Lecture Notes in Computer Science, 12097, 377-385, 2020
• Backward Error Measures for Roots of Polynomials (2020 with Simon Telen and Marc Van Barel). Numerical Algorithms.
• 3264 Conics in a Second (2020, with Paul Breiding and Bernd Sturmfels). Notices of the American Mathematical Society 67 30-37 .
• HomotopyContinuation.jl: A package for homotopy continuation in Julia (2018 with Paul Breiding). Mathematical Software – ICMS 2018. Lecture Notes in Computer Science, 10931, 458-465, 2018

Preprints

• Certifying zeros of polynomial systems using interval arithmetic (2020, with Paul Breiding and Kemal Rose), arXiv:2011.05000.

Ph.D. Thesis

I wrote my Ph.D. thesis entitled Numerical Nolinear Algebra under the supervision of Michael Joswig and Bernd Sturmfels. It is available here.

Software Projects

• HomotopyContinuation.jl: A Julia package for the numerical solution of polynomial systems by homotopy continuation methods.
• Polymake.jl: A Julia interface to polymake.
• MixedSubdivisions.jl: A Julia package for computing a (fine) mixed subdivision and the mixed volume of lattice polytopes.
• PolynomialAmoebas.jl: Visualization and computations related to Amoebas in 2 and 3 variables.