This (second) talk gives an introduction to differential Galois theory, which is a Galois theory for linear homogeneous differential equations. It focuses on the inverse problem: Which groups occur as differential Galois groups over a given field? Key cases include fields F = K(x), where K is algebraically closed or of the form K=k((t)). We generalize the patching methods introduced in the first talk to this situation, and show how these yield answers to the inverse problem. (Note: This second talk is on joint work with David Harbater. It is motivated by the first talk and generalizes methods presented there, but it can be understood independently.)
Deformation Theory Seminar
Wednesday, December 6, 2006 - 3:00pm
Julia Hartmann
Penn and Univ. of Heidelberg