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The Kolchin Seminar in Differential Algebra

Hunter College - Room HW706

Saturday October 18th 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
Differential equations integrable by algebraic geometry: two open directions
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
Cyclic vectors
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

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