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SUMMARY:Some Remarks on Novikovâ€™s Problem for Foliations on Surfaces and
Arnoux-Rauzy Interval Exchange Transformations
DTSTART;VALUE=DATE-TIME:20201012T134500Z
DTEND;VALUE=DATE-TIME:20201012T150000Z
DTSTAMP;VALUE=DATE-TIME:20210922T165840Z
UID:indico-event-6109@indico.math.cnrs.fr
DESCRIPTION:I will discuss some questions related to Novikov's problem for
foliations on surfaces.\n\nThe problem is the following. Let M be a 3-per
iodic surface and H a plane intersecting M. Which kind of curves are reali
zed as the intersection of M and H?\n\nThis problem was formulated by Serg
ey Petrovitch Novikov in the 80's. He conjectured that the "trivial" situa
tions (periodic and integrable) are generic. I will discuss the simplest s
ituation when M is very symmetric. In this case\, with Dynnikov and Skripc
henko\, we prove that the first return of the foliation induced by H is an
Arnoux-Rauzy interval exchange transformation. I will give some propertie
s of these maps (results with Arnoux\, Cassaigne and Ferenczi). In the mos
t interesting situation\, I will mention a work in progress with Dynnikov\
, Mercat\, Paris-Romaskevich and Skripchenko which is supposed to solve No
vikov's conjecture.\n\nThe talk will be accessible to a broad audience.\n\
nhttps://indico.math.cnrs.fr/event/6109/
LOCATION:IHES Centre de confĂ©rences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/6109/
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