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SUMMARY:Symplectic embeddings and infinite staircases - Tara Holm\, Cornel
 l
DTSTART:20191016T150000Z
DTEND:20191016T160000Z
UID:TALK126694@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:McDuff and Schlenk determined when a four-dimensional symplect
 ic ellipsoid can be symplectically embedded into a four-dimensional ball\,
  and found that if the ellipsoid is close to round\, the answer is given b
 y an ``infinite staircase" determined by the odd index Fibonacci numbers\,
  while if the ellipsoid is sufficiently stretched\, all obstructions vanis
 h except for the volume obstruction. Infinite staircases have also been fo
 und when embedding ellipsoids into polydisks (Frenkel - Muller) and into t
 he ellipsoid E(2\, 3) (Cristofaro-Gardiner - Kleinman). In this talk\, we 
 will see how the sharpness of ECH capacities for embedding of ellipsoids i
 mplies the existence of infinite staircases for these and three other targ
 et spaces.  We will then discuss the relationship with toric varieties\, l
 attice point counting\, and the Philadelphia subway system. This is joint 
 work with Dan Cristofaro-Gardiner\, Alessia Mandini\, and Ana Rita Pires.
LOCATION:MR13
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