Numerical methods for working with polynomial systems

Abstract: Whether testing conjectures in algebraic geometry or trying to solve polynomial systems for some application, numerical methods are sometimes a useful alternative to well-known symbolic algorithms. This talk is intended to introduce some of the main tools of the field of numerical algebraic geometry, including homotopy continuation and the numerical irreducible decomposition. In particular, given a polynomial system, we will see how numerical methods can provide floating point approximations to points on each irreducible component of the corresponding complex variety. We will also visit a few recent uses of these methods and consider the benefits and drawbacks compared to exact, symbolic methods.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html