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Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) November 27, 2012 (03:45 PM PST - 06:00 PM PST)
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Location: UC Berkeley
Speaker(s) Adam Boocher, Franz Winkler
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UC Berkeley
Commutative Algebra and Algebraic Geometry Seminar
November 27, 2012
939 Evans Hall

3:45PM: Algebraic ordinary differential equations: General rational solutions and classification

Franz Winkler, Research Institute for Symbolic Computation (RISC) , J. Kepler University Linz, Austria

Consider an algebraic ODE (AODE) of the form $F(x,y,y\\')=0$, where $F$ is a tri-variate polynomial, and $y\\' = \frac{dy}{dx}$. The polynomial $F$ defines an algebraic surface, which we assume to admit a rational parametrization. Based on such a parametrization we can generically determine the existence of a rational general solution, and, in the positive case, also compute one. This method depends crucially on curve and surface parametrization and the determination of rational invariant algebraic curves. Further research is directed towards a classification of AODEs w.r.t. groups of transformations (affine, birational) preserving rational solvability.

5:00PM: Golod Algebras
Adam Boocher

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