May 2nd, 2023

Ana Rita Pires (University of Edinburgh)

Title
Infinite staircases in the symplectic ball packing problem

Abstract
The symplectic version of the problem of packing K balls into a ball in the densest way possible (in 4 dimensions) can be extended to that of symplectically embedding an ellipsoid into a ball as small as possible. A classic result due to McDuff and Schlenk asserts that the function that encodes this problem has a remarkable structure: its graph has infinitely many corners, determined by Fibonacci numbers, that fit together to form an infinite staircase.

This ellipsoid embedding function can be equally defined for other targets, and in this talk I discuss for which other targets the function also has an infinite staircase. In the case when these targets can be represented by lattice (moment) polygons, the targets seem to be exactly those whose polygon is reflexive (i.e., has one interior lattice point). In a specific family of irrational polygons, the answer involves self-similar behavior akin to the Cantor set.

This talk is based on various projects, joint with Dan Cristofaro-Gardiner, Tara Holm, Alessia Mandini, Maria Bertozzi, Tara Holm, Emily Maw, Dusa McDuff, Grace Mwakyoma, Morgan Weiler, and Nicki Magill.

Schedule

10:00 - 11:30 RTG Lecture 1 (Zachary Greenberg) | 5. OG, Konferenzraum

11:30 - 12:00 Get-Together with speaker | 5. OG, Konferenzraum

12:00 - 13:00 Common lunch | reserved at BräuStadel

13:00 - 13:30 Informal meeting of PhD students | 5. OG, Common Room

13:30 - 14:30 RTG colloquium: Prof. Ana Rita Pires | EG Seminarraum B

14:30 - 15:30 Common tea | 5. OG, Common Room

 15:30 - 17:00 RTG Lecture 2 (Julia Heller)| 5. OG, Konferenzraum

HD