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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Squeezing Lagrangian tori in R^4 - Emmanuel Opsht
ein\, Strasbourg
DTSTART;TZID=Europe/London:20190501T160000
DTEND;TZID=Europe/London:20190501T170000
UID:TALK122038AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/122038
DESCRIPTION:A general framework for the talk may be called the
"quantitative geometry" of Lagrangian submanifold
s. I will consider here in which extent a standard
Lagrangian torus in R^4 can be squeezed into a s
mall ball. The result is quite surprising. When t
he ratio between a and b is less than 2\, the spli
t torus T(a\,b) is completely rigid\, and cannot b
e squeezed into B(a+b) by any Hamiltonian isotopy.
When this ratio exceeds 2 on the contrary\, flexi
bility shows up\, and T(a\,b) can be squeezed into
the ball B(3a). The methods of proofs rely on str
etching the neck\, and a good knowledge about holo
morphic curves in dimension 4. This is a joint wor
k with Richard Hind.
LOCATION:MR13
CONTACT:Ivan Smith
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