16 Aug 2006; Mat-Nat Faculty (UiTø), room U1=A228. Wednesday 10:15-12:00

Boris Kruglikov

"Dimension of the solutions space"

It is not clear what we should mean by the solutions space of a system of PDEs, but I discuss what we should call its functional dimension (usually dimension is infinite, so we should "measure" dimension over the space of functions). I will argue how to relate this to the Hilbert function of the corresponding symbolic module and to Cartan's numbers in his famous test for involutivity. Moreover for a system of generalized complete intersection type I will give the formula for this functional dimension.