BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tara Holm (Cornell University) DTSTART:20200630T160000Z DTEND:20200630T170000Z DTSTAMP:20260423T022628Z UID:Geolis/7 DESCRIPTION:Title: S ymplectic embeddings and infinite staircases\nby Tara Holm (Cornell Un iversity) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nMcDuff and S chlenk determined when a four-dimensional symplectic ellipsoid can be symp lectically embedded into a four-dimensional ball. They found that if the e llipsoid is close to round\, the answer is given by an infinite staircase determined by Fibonacci numbers\, while if the ellipsoid is sufficiently s tretched\, all obstructions vanish except for the volume obstruction. Infi nite staircases have also been found when embedding ellipsoids into polydi sks (Frenkel - Muller\, Usher) and into the ellipsoid E(2\,3) (Cristofaro- Gardiner - Kleinman). We will describe a general approach to the question of when embedding ellipsoids into a toric target has an infinite staircase \, where we provide the first obstruction to the existence of a staircase. We use this obstruction to explore infinite staircases for toric symplect ic manifolds\, identifying three new infinite staircases\, and culminating in the conjecture that these are the only toric examples. We will describ e further work-in-progress on ellipsoid embedding functions with more gene ral targets. I will not assume any prior acquaintance with infinite stairc ases and will motivate the talk with plentiful examples and pictures. This talk is based on a number of collaborations with Dan Cristofaro-Gardiner\ , Alessia Mandini\, and Ana Rita Pires\; Maria Bertozzi\, Emily Maw\, Dusa McDuff\, Grace Mwakyoma\, Ana Rita Pires\, Morgan Weiler\; and Nicki Magi ll.\n LOCATION:https://researchseminars.org/talk/Geolis/7/ END:VEVENT END:VCALENDAR