On the reliable computation of the monodromy of a plane algebraic curve.

Dr. Marc Rybowicz, Department of Mathematics, University of Limoges

Wednesday July 13th, 2005 at 3:30pm in K9509.

Abstract: 

The computation of the monodromy of an algebraic curve can be viewed as
a first step towards an effective Abel-Jacobi theorem. Besides, the
monodromy provides algebraic information about the function field of the
curve since it is isomorphic to the Galois group of the extension field.

The monodromy command of Maple's algcurves package has some flaws since
it relies on heuristics and an empirical control of the numerical
computations involved in the process.

In this talk, we will report on some investigations of a reliable
approach based on a theorem by B. Smith. This is joint work with Mark Van Hoeij.

Our motivation comes from the indefinite integration of algebraic
functions and other computer algebra problems. We will briefly explain them.