Integrable systems with S^1-actions and the associated polygons

Abstract: Semitoric systems are a type of four-dimensional integrable system which admit a global $S^1$-action; these systems were classified by Pelayo and Vu Ngoc in 2011, generalizing the classification of toric integrable systems and making use of an invariant called a `semitoric polygon'. I will present some results about bifurcations of such systems, and show how this can be used to construct explicit examples of such systems associated to certain given semitoric polygon. Time permitting, I will also discuss how hypersemitoric systems, a generalization of semitoric systems, appear in this context. Some of the results I will present are joint with Yohann Le Floch and Sonja Hohloch.

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