Cohomology in algebra, geometry, physicsand statistics

Around the noncommutative cross ratio

The cross-ratio of four points on a projective line is one of the most important projective invariants, which finds most unexpected applications throughout Mathematics from Geometry and Topology to the Integrable systems theory. I will tell, how one can widen the domain on which this invariant is defined so as to allow one consider "projective lines" over noncommutative field. It turns out that there is an approach, which allows one find such generalization so that most of important properties of the cross ratio are preserved. Study of this new object is an interesting new problem. Based on joint work with V.Retakh and V.Rubtsov.

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