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SUMMARY:Lagrangian Klein bottles in $S^2\\times S^2$
DTSTART:20261023T091500Z
DTEND:20261023T101500Z
DTSTAMP:20261015T123300Z
UID:indico-event-17031@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nikolaos Adaloglou (Jussieu)\n\nThe study of Lagrang
 ian submanifolds is a central theme insymplectic geometry. In this tal
 k\, after a brief introduction on thebasics of symplectic geometr
 y\, we are going to study Lagrangiansubmanifolds in $S^2\\times S
 ^2$\, equipped with standard symplecticforms. Our goal is to understan
 d which symplectic forms on $S^2\\times S^2$carry Lagrangian Klein bott
 les. We will focus mainly on constructingthe Klein bottles\, usin
 g certain techniques from the theory of Lagrangiantorus fibrations
 . This theory effectively reduces many constructiveproblems into p
 roblems of classical affine geometry of the plane.Afterwards\, I 
 will explain how to obstruct the existence of someLagrangian Klei
 n bottles\, using pseudoholomorphic curve techniques.Together\, the
  obstructive part and the constructive part completelydetermine wh
 ich symplectic forms in $S^2\\times S^2$ carry a LagrangianKlein 
 bottle.This is joint work with J. Evans and work in progress with Evans an
 d J. Hauber.\n\nhttps://indico.math.cnrs.fr/event/17031/
LOCATION:112 (ICJ)
URL:https://indico.math.cnrs.fr/event/17031/
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