On the reliable computation of the monodromy of a plane algebraic curve.
Dr. Marc Rybowicz, Department of Mathematics, University of Limoges
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.