A tale of two widths: lattice and Gromov
Ben Wormleighton (Washington)
Abstract: To a polytope $P$ whose facet normals are rational one can associate two geometric objects: a symplectic toric domain $X_P$ and a polarised toric algebraic variety $Y_P$, which can also be viewed as a potentially singular symplectic space. A basic invariant of a symplectic manifold $X$ is its Gromov width: essentially the size of the largest ball that can be 'symplectically' embedded in $X$. A conjecture of Averkov-Hofscheier-Nill proposed a combinatorial bound for the Gromov width of $Y_P$, which I recently verified in dimension two with Julian Chaidez. I’ll discuss the proof, which goes via various symplectic and algebraic invariants with winsome combinatorial interpretations in the toric case. If there’s time, I’ll discuss ongoing work and new challenges for a similar result in higher dimensions.
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
| Organizers: | Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi |
| *contact for this listing |