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SUMMARY:Point-Counting and the Zilber-Pink Conjecture
DTSTART:20240305T093000Z
DTEND:20240305T113000Z
DTSTAMP:20240522T112900Z
UID:indico-event-11339@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Jonathan Pila (University of Oxford & IHES)\n\nThe Z
ilber-Pink conjecture is a diophantine finiteness conjecture. It unifies a
nd gives a far-reaching generalization of the classical Mordell-Lang and A
ndre-Oort conjectures\, and is wide open in general.Point-counting results
for definable sets in o-minimal structures provide a strategy for proving
suitable cases which has had some success\, in particular in its use in p
roving the Andre-Oort conjecture.The course will describe the Zilber-Pink
conjecture and the point-counting approach to proving cases of it\, eventu
ally concentrating on the case of a curve in a power of the modular curve.
We will describe the model-theoretic contexts of the conjectures and techn
iques\, and the essential arithmetic ingredients.\n\nhttps://indico.math.c
nrs.fr/event/11339/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/11339/
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