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BEGIN:VEVENT
DTSTAMP:20241122T160731Z
DTSTART:20241127T151500Z
DTEND:20241127T163000Z
SUMMARY:Logic seminar: Alex Wilkie
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}eyt-m2bo8w8
 w-xh4g3x
DESCRIPTION:ON ZILBER'S QUASIMINIMALITY CONJECTURE: AN ANALYTIC APPROACH\
 n\nThis conjecture concerns the expansion \\mathbb{C}_{exp} of the compl
 ex exponential field by the usual complex exponential function and asser
 ts that every definable subset of the complex numbers  in this structure
  (even by a formula of the infinitary language allowing countable conjun
 ctions and disjunctions) is either countable or co-countable\, i.e. that
  \\mathbb{C}_{exp} is quasiminimal. Now notions of minimality abound in 
 model theory and often give rise to pregeometries\, i.e. closure operato
 rs satisfying an exchange property which\, in analytic situations\, amou
 nts to an inverse function theorem. I will clarify this remark in the co
 ntext of Zilber's conjecture and then go on to discuss how it gives rise
  to a natural (Logic free) analytic continuation  statement that implies
  a positive answer to Zilber's conjecture. I hope that there will be tim
 e left to mention some variants of this statement\, in particular one co
 ncerning the solutions of ordinary differential equations of the form X'
  = P(X) where P is a polynomial map.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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