**The Kolchin Seminar in Differential Algebra
**

**Saturday October
18**^{th}** 2003**

**Emma Previato**

Boston University

**Differential equations integrable by algebraic geometry:
a survey of methods**

2:00 - 3:00PM

**Abstract:**
Two geometric structures for certain (hierarchies of)
integrable PDEs emerged in the late 1960s and through the 1970s:
a (finite-genus) spectral curve and its theta functions; and
an infinite Grassmannian. This talk will provide the setting
to construct exact solutions to the KdV and KP equations,
by the theta function of the spectral curve and the tau function
associated to the determinant bundle over the Grassmannian.

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** Emma Previato**Boston University

and their interpretation in differential algebra

3:30 - 4:30PM

**Abstract:**
Building on the previous talk, we will present two
generalizations of the spectral curve and Grassmannian constructions,
higher-rank and multi-variable, together with several open
questions of implementation and some examples. These can be posed
in the realm of differential algebra.

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**Richard C. Churchill
**Hunter College

5:00 - 6:00 PM

**Abstract:**
A cyclic vector can be regarded as a mechanism for converting a
system of n first-order ODEs to nth-order form. I will explain this
viewpoint in the talk and present an algorithm, developed jointly with
J.J. Kovacic, for constructing such vectors. The presentation will be
both elementary and introductory. In particular, no background in
differential algebra will be assumed.

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

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