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Speaker:
Marius van der Put
Zugehörigkeit:
Groningen University
Datum:
Mit, 18/04/2018 - 14:30 - 15:30
Location:
MPIM Lecture Hall
Parent event:
MPIM/HIM-Number theory lunch seminar We consider a first order differential equation of the form $f(y'; y) = 0$ with $f\in K[S; T]$ and $K$ a
differential field either complex or of positive characteristic. We investigate several properties of $f$,
namely the 'Painlevé property' (PP), solvability and stratification. A modern proof of the classication
of first order equations with PP is presented for all characteristics. A version of the Grothendieck-Katz
conjecture for first order equations is proposed and proven for special cases. Finally the relation with
Malgrange's Galois groupoids and model theory is discussed.
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