N&O Seminar: Simon Telen (MPI Leipzig)

Everyone is welcome to attend the online N&O seminar with Simon Telen (MPI Leipzig). Title: Eigenvalue methods for solving polynomial systems. Please contact Daniel Dadush for the zoom link.
  • What Networks & Optimization Not a Seminar English Seminars
  • When 17-03-2021 from 14:00 to 15:00 (Europe/Amsterdam / UTC100)
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Everyone is welcome to attend the online N&O seminar with Simon Telen (MPI Leipzig). Title: Eigenvalue methods for solving polynomial systems.

Abstract:
The problem of computing the isolated solutions to a system of polynomial equations can be translated into an eigenvalue problem. Standard methods for performing this translation, such as Groebner basis algorithms, may lead to a drastic amplification of rounding errors. This renders the approach unfeasible for floating point computations. In this talk I will discuss two important remedies. On the one hand, it is crucial to make a good choice for the basis of the coordinate ring of the finite solution set. Secondly, working in an appropriate, compact space allows us to deal with ‘solutions at infinity’ in a robust manner. This leads to interesting questions related to the regularity of homogeneous ideals in Cox rings. I will show that, although classical methods fail at intersecting two degree 15 plane curves, we can accurately compute the 28900 intersection points of two degree 170 curves using these new techniques.


Please contact Daniel Dadush for the zoom link.