Cross-ratios and perfect matchings

Abstract: Given a bipartite graph G (subject to a constraint), the "cross-ratio degree" of G is a non-negative integer invariant of G, defined via a simple counting problem in algebraic geometry. I will discuss some natural contexts in which cross-ratio degrees arise. I will then present a perhaps-surprising upper bound on cross-ratio degrees in terms of counting perfect matchings. Finally, time permitting, I may discuss the tropical side of the story.

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