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UID:calendar.2335913.field_date.0@mathematics.huji.ac.il
DTSTAMP:20210124T030416Z
CREATED:20201222T230031Z
DESCRIPTION:Date: \n\n4:00pm to 5:15pm\n\n\n\n\nSee also: Seminars\, Even
ts & Seminars\, Basic NotionsLocation: \n\nZoom\n\n\n\n\n A family of prob
lems in Diophantine geometry has the followingform: We fix a collection of
'special' algebraic varieties among which the0-dimensional are called 'sp
ecial points'. Mostly\, if V is a special varietythen the special points a
re Zariski dense in V\, and the problem is to provethe converse: If V is a
n irreducible algebraic variety and the specialpoints are Zariski dense in
V then V itself is special.Particular cases of the above are the Manin-Mu
mford conjecture(where the special varieties are certain cosets of abelian
sub-varieties andthe special points are torsion points)\, the Mordell-La
ng conjecture\, the Andre-Oort Conjecture. In 1990's Hrushovski showed how
methods of model theory could be applied to solve certain such problems.
About 10 years ago Pila and Zannier developed a different framework which
allows to apply model theory and especially the theory of o-minimal struc
tures\, to tackle questions of this nature over the complex numbers. Pila
used these methods to prove some open cases of the Andre-Oort conjecture
and since then there was an influx of articles which use similar technique
s. At the heartof the Pila-Zannier method lies a theorem of Pila and Wilki
e on rationalpoints on so-called definable sets in o-minimal structures.In
these survey talks I will describe the basic mode theoretic ingredients o
fthe Pila-Zannier method and the way in which it is applied. Iwill not ass
ume prior knowledge of model theory or Logic and will try toexplain all no
tions which may come up.\n\nZoom link:\n\nhttps://huji.zoom.us/j/871310223
02?pwd=SnRwSFRDNXZ4QVFKSnJ1Wit2cjZtdz09\n\n Export\n \n\n \nsubscribe i
Cal
DTSTART;TZID=Asia/Jerusalem:20210114T160000
DTEND;TZID=Asia/Jerusalem:20210114T171500
LAST-MODIFIED:20201222T230031Z
SUMMARY:Basic Notions: Kobi Peterzil (U. of Haifa) 'The Pila-Zannier method
: applications of model theory to Diophantine geometry'.
URL;TYPE=URI:https://mathematics.huji.ac.il/event/basic-notions-kobi-peterz
il-u-haifa-pila-zannier-method-applications-model-theory
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