Hauptseminar Geometrie

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, Emily Maw, Dusa McDuff, Grace Mwakyoma, Morgan Weiler, and Nicki Magill.

Dienstag, den 2. Mai 2023 um 13:30 Uhr, in INF205, SRB Dienstag, den 2. Mai 2023 at 13:30, in INF205, SRB

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Beatrice Pozzetti, Prof. Peter Albers