BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ana Rita Pires (University of Edinburgh) DTSTART:20250218T150000Z DTEND:20250218T160000Z DTSTAMP:20260423T022719Z UID:Geolis/164 DESCRIPTION:Title: Infinite staircases in ball packing problems\nby Ana Rita Pires (Univ ersity of Edinburgh) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nT he 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 symplec tically embedding an ellipsoid into a ball as small as possible. A classic result due to McDuff and Schlenk asserts that the function that encodes t his problem has a remarkable structure: its graph has infinitely many corn ers\, determined by Fibonacci numbers\, that fit together to form an infin ite staircase.\n\nThis ellipsoid embedding function can be equally defined for other targets\, and this talk will be about other targets for which t he function has and does not have an infinite staircase. Firstly we will s ee how in the case when these targets have lattice moment polygons\, the t argets with infinite staircases seem to be exactly those whose polygon is reflexive (i.e.\, has one interior lattice point). Secondly\, we will look at the family of one-point blowups of CP^2\, where the answer involves se lf-similar behaviour akin to the Cantor set.\n\nThis talk is based on vari ous projects\, joint with Dan Cristofaro-Gardiner\, Tara Holm\, Alessia Ma ndini\, Maria Bertozzi\, Tara Holm\, Emily Maw\, Dusa McDuff\, Grace Mwaky oma\, Morgan Weiler\, and Nicki Magill.\n LOCATION:https://researchseminars.org/talk/Geolis/164/ END:VEVENT END:VCALENDAR