## View abstract

### 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. document.getElementById('cloak02e45b8a991a178a42974acc5e09b360').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy02e45b8a991a178a42974acc5e09b360 = 'w&#105;bm&#101;r' + '&#64;'; addy02e45b8a991a178a42974acc5e09b360 = addy02e45b8a991a178a42974acc5e09b360 + 'm&#97;th' + '&#46;' + 't&#117;gr&#97;z' + '&#46;' + '&#97;t'; var addy_text02e45b8a991a178a42974acc5e09b360 = 'w&#105;bm&#101;r' + '&#64;' + 'm&#97;th' + '&#46;' + 't&#117;gr&#97;z' + '&#46;' + '&#97;t';document.getElementById('cloak02e45b8a991a178a42974acc5e09b360').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy02e45b8a991a178a42974acc5e09b360 + '\'>'+addy_text02e45b8a991a178a42974acc5e09b360+'<\/a>';

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.