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SUMMARY:Squeezing Lagrangian tori in R^4	 - Emmanuel Opshtein\, Strasbourg
DTSTART:20190501T150000Z
DTEND:20190501T160000Z
UID:TALK122038@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:A general framework for the talk may be called the "quantitati
 ve geometry" of Lagrangian submanifolds. I will consider here in which ext
 ent a standard Lagrangian torus in R^4 can be squeezed  into a small ball.
  The result is quite surprising. When  the ratio between a and b is less t
 han 2\, the split torus T(a\,b) is completely rigid\, and cannot be squeez
 ed into B(a+b) by any Hamiltonian isotopy. When this ratio exceeds 2 on th
 e contrary\, flexibility shows up\, and T(a\,b) can be squeezed into the b
 all B(3a). The methods of proofs rely on stretching the neck\, and a good 
 knowledge about holomorphic curves in dimension 4. This is a joint work wi
 th Richard Hind.   
LOCATION:MR13
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