Session III.6 - Symbolic Analysis
Monday, June 19, 15:00 ~ 15:30
Regular singular differential equations and free proalgebraic groups
Michael Wibmer
Graz University of Technology, Austria - This email address is being protected from spambots. You need JavaScript enabled to view it.
Let $S$ be a finite subset of the Riemann sphere. It is an immediate consequence of the Riemann-Hilbert correspondence that the differential Galois group of the family of all regular singular differential equations with singularities inside $S$ is the proalgebraic completion of the free group on $|S|-1$ generators . In this talk we will discuss generalizations of this statement to infinite $S$. In particular, we will determine the differential Galois group of the family of all regular singular differential equations on the Riemann sphere.