**SMS scnews item created by Martina Chirilus-Bruckner at Tue 29 Apr 2014 1213**

Type: Seminar

Distribution: World

Expiry: 9 May 2014

**Calendar1: 2 May 2014 1400-1500**

**CalLoc1: Carslaw 175**

CalTitle1: Joint Colloquium Sydney–UNSW: Viktoria Heu -- Some aspects of the Riemann-Hilbert correspondence

Auth: martinac@pmartinac2.pc (assumed)

### Joint Colloquium Sydney–UNSW

# Some aspects of the Riemann-Hilbert correspondence

### Viktoria Heu (IRMA, University of Strasbourg)

Date:

** Fri, 02/05/2014 - 2:00pm **

Location:

** Carslaw Building, Lecture Theatre 175, University of Sydney **

Speaker:

** Viktoria Heu **

Title:

** Some aspects of the Riemann-Hilbert correspondence **

Abstract:

To any system of meromorphic linear differential equations on the Riemann sphere, we can associate a representation of the fundamental group of the punctured sphere, the so-called monodromy representation, measuring the dynamics of the solutions. Roughly speaking, the Riemann-Hilbert problem asks whether any representation can be obtained in this way. The answer to this problem highly depends on its precise statement in different contexts. We investigate the following angle : conveniently patching together local systems of differential equations with respect to the monodromy, we obtain a so called ''connection'' on a vector bundle, given by the global patching. What can be said about this vector bundle ?