Moscow--Petersburg seminar on low-dimensional mathematics
SPb, PDMI, 14.12.2001, 16:00--17:45, room 311

I.S.Krasilschik
Geometry of differential equations and their algebraic invariants.

Modern geometrical theory of differential equations treats an equation
as a submanifold in a jet space endowed with a characteristic
distribution, the so-called Cartan distribution. 
When one considers prolongations of a given equation, dimensions of the 
corresponding distributions tend to infinity. Nevertheless, at the top 
level (the infinite prolongation) this dimension "shrinks" to a finite 
number, the number of independent variables. For the majority of 
integrable systems this number is 2.

We plan to present a concise review of the basic geometrical structures
underlying differential equations and discuss their algebraic (mostly
cohomological) invariants.

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Seminar home page: http://www.pdmi.ras.ru/~duzhin/LDM/