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BEGIN:VEVENT
DTSTAMP:20191031T113137Z
DTSTART:20191106T150000Z
DTEND:20191106T160000Z
SUMMARY:Omar Leon Sanchez - Existence of PPV-extensions over differentia
lly large fields.
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}z38-k2emp52
0-uk8dfr
DESCRIPTION:Join us for this seminar\, part of the Logic Seminar Series.
Note the unusual room: University Place 3.213\n\nIn a 2016 paper\, Cresp
o\, Hajto\, and van der Put proved that if a differential field (K\,d) i
s real (or p-adic) and its constant subfield C_K is real closed (respect
ively p-adically closed) then any homogeneous linear differential equati
on over K has a Picard-Vessiot extension which is real (respectively p-a
dic). Turns out that this type of existence result holds as long as C_K
is existentially closed in K (as fields) and the first Galois cohomology
of C_K is finite for any linear algebraic group (so\, by a classical re
sult of Serre\, it suffices for C_K to be bounded as a field). This was
observed in a paper of Kamensky and Pillay\, who provided a model-theore
tic proof (other proofs use the Tannakian formalism). In this talk I wil
l give an overview of the model-theoretic proof and explain how one can
attempt to extend the argument to show existence of Parameterized Picard
-Vessiot (PPV) extensions\; there are some subtleties of course that hav
e to do with differential Galois cohomology and so at this point we assu
me differential largeness. All definitions will be explained. This is jo
int (but separate) work with J. Nagloo\, A. Pillay\, and M. Tressl.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:3.213\, University Place\, Manchester
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