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UID:6468@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210401T140000
DTEND;TZID=Europe/Paris:20210401T150000
DTSTAMP:20250118T133116Z
URL:https://www.i2m.univ-amu.fr/evenements/non-archimedean-analogue-of-wil
 kies-conjecture-and-point-counting-from-pfaffian-over-subanalytic-to-hense
 l-minimal/
SUMMARY:Raf Cluckers (University of Lille\, France and KU Leuven\, Belgium)
 : Non-archimedean analogue of Wilkie's conjecture and point counting\, fro
 m Pfaffian over subanalytic to Hensel minimal
DESCRIPTION:Raf Cluckers: \n\n\n\n\n\n\n\n\n\nPoint counting on definable s
 ets in non-archimedean settings has many faces. (All mimicking some aspect
 s of point counting in o-minimal settings.) For sets living in Q_p^n\, one
  can count actual rational points of bounded height\, but for sets in C((t
 ))^n\, one rather "counts" the polynomials in t of bounded degree. What if
  the latter is of infinite cardinality? We treat three settings\, each wit
 h completely different behaviour for point counting :\n1) the setting of s
 ubanalytic sets\, where we show finiteness of point counting but growth ca
 n be aribitrarily fast with the degree in t \;\n2) the setting of Pfaffian
  sets\, which is new in the non-archimedean world and for which we show an
  analogue of Wilkie's conjecture in all dimensions\;\n3) the Hensel minima
 l setting\, which is most general and where finiteness starts to fail\, ev
 en for definable transcendental curves! In this infinite case\, one bounds
  the dimension rather than the (infinite) cardinality.\nThis represents jo
 int work with Binyamini\, Novikov\, with Halupczok\, Rideau\, Vermeulen\, 
 and separate work by Cantoral-Farfan\, Nguyen\, Vermeulen. Of course\, ana
 logues to Yomdin-Gromov C^r parameterizations\, and to bounds à la Gabrie
 lov for Pfaffian sets play roles.\n\n\n\n\n\n\n\n\n\n\n\nhttps://arxiv.org
 /abs/2009.05480\n\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/04/Raf_Cluckers.jpg
CATEGORIES:Groupe de travail,Singularités,Virtual event
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