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First order differential equations

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Marius van der Put
Groningen University
Wed, 2018-04-18 14:30 - 15:30
MPIM Lecture Hall

We consider a fi rst order differential equation of  the form $f(y'; y) = 0$ with $f\in K[S; T]$ and $K$ a
differential fi eld either complex or of positive characteristic.  We investigate several properties of $f$,
namely the 'Painlevé property' (PP), solvability and stratifi cation. A modern proof of the classi cation
of fi rst order equations with PP is presented for all characteristics. A version of the Grothendieck-Katz
conjecture for fi rst 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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