Design of Algorithms for the Construction of Differential Equations with a Given Finite Galois Group
Sonja Lauer ( Universität Karlsruhe )
Thursday, February, 23th, 2006, 1400, b-it 1.25 (cosec meeting room)
Contents
Analogously to the inverse problem of classical Galois theory, the inverse problem of differential Galois theory deals with groups which occur as differential Galois groups of a linear differential equation. Tretkoff and Tretkoff's (1979) findings imply that each finite group is isomorphic to a differential Galois group of a linear differential equation over C(x). With such differential equation one can construct a polynomial over C(x)[y], whose classical Galois group equals the differential Galois group of this differential equation and which is hence isomorphic to the originating group. Van der Put and Ulmer (2000) describe a method to construct a differential equation with a given finite group. I show algorithms based on this method and demonstrate some example calculations for certain groups.