Computational Algebra Seminar: Winkler -- Classification of algebraic differential equationsw.r.t. rational solvability

Speaker: Franz Winkler (RISC-Linz)
Title: Classification of algebraic differential equations w.r.t. rational solvability
Time & Place: 3:05-4pm, Thursday 21 February, Carslaw 535

Abstract:
Consider an algebraic ordinary differential equation (AODE), i.e. a
polynomial relation between the unknown function and its derivatives.
This polynomial defines an algebraic hypersurface.  By considering
rational parametrizations of this hypersurface, we can decide the
rational solvability of the given AODE, and in fact compute the general
rational solution.  This method depends crucially on curve and surface
parametrization and the determination of rational invariant algebraic
curves. Transforming the ambient space by some group of transformations,
we get a classification of AODEs, such that equivalent equations share
the property of rational solvability. In particular we discuss
affine and birational transformation groups.