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SUMMARY:Tame Geometry and Hodge Theory
DTSTART;VALUE=DATE-TIME:20200225T093000Z
DTEND;VALUE=DATE-TIME:20200225T113000Z
DTSTAMP;VALUE=DATE-TIME:20200811T140123Z
UID:indico-event-4975@indico.math.cnrs.fr
DESCRIPTION: \n\nHodge theory\, as developed by Deligne and Griffiths\, i
s the main tool for analyzing the geometry and arithmetic of complex algeb
raic varieties. It is an essential fact that at heart\, Hodge theory is NO
T algebraic. On the other hand\, according to both the Hodge conjecture an
d the Grothendieck period conjecture\, this transcendence is severely cons
trained.\n\n \n\nTame geometry\, whose idea was introduced by Grothendiec
k in the 80s\, seems a natural setting for understanding these constraints
. Tame geometry\, developed by model theorists as o-minimal geometry\, has
for prototype real semi-algebraic geometry\, but is much richer. It studi
es structures where every definable set has a finite geometric complexity.
\n\n \n\nThe aim of this course is to present a number of recent applicat
ions of tame geometry to several problems related to Hodge theory and peri
ods. After recalling basics on o-minimal structures and their tameness pro
perties\, I will discuss:\n- the use of tame geometry in proving algebraiz
ation results (Pila-Wilkie theorem\; o-minimal Chow and GAGA theorems in d
efinable complex analytic geometry)\;\n- the tameness of period maps\; alg
ebraicity of images of period maps\;\n- functional transcendence results:
Ax-Schanuel conjecture from abelian varieties to Shimura varieties and var
iations of Hodge structures. Applications to atypical intersections (Andr
é-Oort conjecture and Zilber-Pink conjecture)\;\n- the geometry of Hodge
loci and their closures.\n\n \n\nhttps://indico.math.cnrs.fr/event/4975/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4975/
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