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SUMMARY:Bi-Lagrangian Structures and Teichmüller Theory
DTSTART;VALUE=DATE-TIME:20180618T143000Z
DTEND;VALUE=DATE-TIME:20180618T154500Z
DTSTAMP;VALUE=DATE-TIME:20210414T023947Z
UID:indico-event-3509@indico.math.cnrs.fr
DESCRIPTION:A bi-Lagrangian structure on a manifold is the data of a sympl
ectic form and a pair of transverse Lagrangian foliations. Equivalently\,
it can be defined as a para-Kähler structure\, i.e. the para-complex anal
og of a Kähler structure. After discussing interesting features of bi-Lag
rangian structures in the real and complex settings\, I will show that the
complexification of any Kähler manifold has a natural complex bi-Lagrang
ian structure. I will then specialize this discussion to moduli spaces of
geometric structures on surfaces\, which typically have a rich symplectic
geometry. We will see that that some of the recognized geometric features
of these moduli spaces are formal consequences of the general theory while
revealing new other features\, and derive a few well-known results of Tei
chmüller theory. Time permitting\, I will present the construction of an
almost hyper-Kähler structure in the complexification of any Kähler mani
fold. This is joint work with Andy Sanders.\n\nhttps://indico.math.cnrs.fr
/event/3509/
LOCATION:IHES Centre de conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/3509/
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