Computing discriminant complements using pseudo-witness sets

Date

Oct 23, 2025

Time

3:00 PM - 4:00 PM

Speaker

Oskar Henriksson

Affiliation

MPI-CBG

Language

en

Main Topic

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Description

A key object for understanding a parametrized polynomial system is the discriminant variety, which divides the parameter space into regions of constant qualitative and quantitative properties of the solution sets. However, a common challenge in the study of discriminant varieties is that many methods rely on having access to explicit equations, which in general requires solving a costly implicitization problem. In this work, we present a new approach for finding sample points in all connected components of the complement of discriminant varieties, which combines the recent Hypersurfaces.jl package with the framework of pseudo-witness sets in a way that allows us to circumvent the need for symbolic elimination. This is joint work in progress with Paul Breiding, John Cobb, Aviva Englander, Nayda Farnsworth, Jon Hauenstein, David Johnson, Jordy Garcia, and Deepak Mundayur.

Last modified: Oct 23, 2025, 7:37:28 AM