**The Kolchin Seminar in
Differential Algebra**

**Saturday May 15**^{th}** 2004**

******************************************

**Andy R. Magid**

University of Oklahoma

**Iterated Picard-Vessiot extensions**

2:00-3:00PM

**Abstract:** The consideration of solutions of differential equations whose
coefficients are solutions of differential equations leads to finite
towers of Picard-Vessiot (or Differential Galois) extensions of a
differential field *F*. While such iterated Picard-Vessiot extensions may
not themselves be even embeddable in a Picard-Vessiot extension, they do
embedd in iterated Picard-Vessiot closures, and the automorphism groups
of these latter, as we show in the main result, may be used to construct a
Galois correspondence for the differential subfields of normal locally
iterated Picard-Vessiot extensions. In the process, we characterize the
differential subfields of the iterated closures.

******************************************

**William Sit**

City College of CUNY

**Some symbolic computation software for differential equations**

3:30-4:30PM

This talk is a preliminary report of an attempt to survey a small portion of recent symbolic computational software of interest to differential algebraists and hopefully also to researchers looking for software for differential equations based on Maple, Mathematica and Axiom. A selected subset of software implementations will be illustrated with examples of systems of differential equations that benefited from these techniques.

The talk is intended for the general scientific public.

******************************************

**Andy R. Magid**

University of Oklahoma

**The construction of Picard-Vessiot closures**

5:00-6:00PM

**Abstract**: There are two basic approaches to the algebraic construction of
Picard-Vessiot closures: one can either construct a maximal extension of
a suitable sort by an application of Zorn's Lemma, and then try to prove
that it contains copies of all Picard-Vessiot extensions of the base; or
one can take a tensor product of all the Picard-Vessiot extensions of the
base and then try to prove than an appropriate quotient exists. (Both
approaches are related, of course.) We follow the second approach. Our
argument proceeds via a class of differential fields which are especially
well adapted for the Zorn's lemma argument we need.It is known that differential
automorphisms of the base field lift to
differential automorphisms of a Picard-Vessiot closure. We give another
proof of that, using the tensor product construction of closures, which
makes this lifting theorem more transparent.

********************************************
**

**Coffee and tea will be served
beginning at 1:30 PM
Room HW706 **

**Click
here for directions to Hunter College and location of room**