Newton–Okounkov bodies and minimal models of cluster varieties

Abstract: I will explain a general procedure to construct Newton–Okounkov bodies for a certain class of (partial) compactifications of cluster varieties. This class consists of the (partial) minimal models of cluster varieties with enough theta functions. This construction applies for example to Grassmannians and Flag varieties, among others. Our construction depends on a choice of torus in the atlas of the cluster variety and the associated Newton–Okounkov body lives inside a real vector space. Time permitting, I will explain how to compare the Newton–Okounkov bodies associated with different tori and elaborate on the "intrinsic Newton–Okounkov body", which is an object that does not depend on the choice of torus and lives inside the real tropicalization of the mirror cluster variety. This is based on upcoming work with Lara Bossinger, Man-Wai Cheung and Timothy Magee.

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