Quebec Mathematical Sciences Colloquium

February 15, 2008 from 16:00 to 18:00 (Montreal/Miami time) On location

Differential Groups and Differential Relations

Colloquium presented by Michael F. Singer (North Carolina State University)

I will present a leisurely introduction to a Galois theory of linear difference equations where the Galois groups are linear differential groups that is, groups of matrices whose entries satisfy a fixed set of polynomial differential equations. These groups measure the differential dependence among solutions of linear difference equations. I will show how this theory can be used to reprove Hšlder's Theorem of 1887 that the Gamma function satisfies no differential polynomial equation as well as new results concerning differential dependence of solutions of higher order difference equations. This is joint work with Charlotte Hardouin.


UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420