# Geometry and Model Theory

*Time: *Friday, November 04, 2011,
14h - 15h30

*Location: *amphithéâtre Rataud

## Inverse problems in the Parameterized Picard-Vessiot Theory

**Michael Singer**
(North Carolina, SU)

The parameterized Picard-Vessiot theory aims at studying the differential behavior of solutions of parameterized linear differential equations. It associates to such an equation a linear differential algebraic group (LDAG), that is, a group of matrices whose entries are functions satisfying a fixed set of differential equations. After giving an introduction to this theory, I will show that not all LDAGs can occur as Galois groups over k(x), the field of rational functions in x whose coefficients are functions of a parameter t and characterize those LDAGs that do occur.