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PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:The Büchi K3 surface and its rational points
DTSTART:20120906T111500
DTEND:20120906T123000
DTSTAMP:20260505T075917Z
UID:b05f6c9299b449481f6518722205dddf2ce025157c1697eea52dea51
CATEGORIES:Conferences - Seminars
DESCRIPTION:Damiano Testa\nIn order to extend Matiyasevich's resolution of
  Hilbert's Tenth Problem\, Büchi introduced a sequence of affine algebrai
 c surfaces: he showed that if the surfaces in this sequence eventually onl
 y have trivial integral solutions\, then the proof of undecidability can b
 e extended to the case of systems of diagonal quadratic equations. Vojta l
 ater showed that a weak form of the Lang's Conjectures implies that\, with
  finitely many exceptions\, the "Büchi surfaces" do indeed only have triv
 ial integral solutions.\nIn my talk I will report on joint work in progres
 s with M. Artebani and A. Laface on the rational (not necessarily integral
 !) points of the first non-rational surface in\nBüchi's sequence. I will 
 mention some of the geometric properties of this surface and show that it 
 is a moduli space of vector bundles. The modular interpretation\nof this p
 roblem naturally leads to a question on integral structures on a moduli sp
 aces of vector bundles\, to which we do not know the answer.\n
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 nem
STATUS:CONFIRMED
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