# PhD Seminar • Symbolic Computation — Solving Structured Determinantal Systems using Homotopy Methods with an Application to Computing Isolated Critical Points for Invariant Systems

Tuesday, December 1, 2020 — 9:00 AM EST

## Please note: This PhD seminar will be given online.

Thi Xuan Vu, PhD candidate
David R. Cheriton School of Computer Science

Supervisors: Professors George Labahn, Éric Schost, Mohab Safey El Din

Given a sequence of polynomials G and a polynomial matrix F, the determinantal system corresponding to G and F is the system of polynomials containing G and all maximal minors of F. These kinds of systems appear frequently in optimization. For example, if $\phi$ is a function and F is the Jacobian matrix of G, together with the extra row corresponding to the gradient of $\phi$ then we find the critical points of $\phi$ over the algebraic variety defined by G.

In this talk, we study how symbolic homotopy methods can be used to solve such systems. In particular, using structures of F such as the total degrees, sparsity, and weighted degrees, to obtain efficient, randomized algorithms having a runtime being polynomial in the bound on the size of the output of our algorithms. We use our results in the determinantal systems combined with weighted domains to compute critical points of maps restricted to algebraic sets when both are completely symmetric in their input variables.

To join this PhD seminar on BigBlueButton, please go to https://webconf.math.cnrs.fr/b/pog-m6h-mec.

Location
Online PhD seminar
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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