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BIRS Workshop Lecture Videos

Complex analogue of the algebra of even valuations on convex sets Alesker, Semyon


The multiplicative structure on translation invariant valuations was introduced by the speaker about 15 years ago. Since than a number of non-trivial properties of this product has been discovered and several applications to integral geometry were found. In this talk we construct a complex analogue of the algebra of even translation invariant valuations and establish several properties of it. The construction and proofs use Radon and cosine transform on complex Grassmannians. If time permits we will describe briefly further analogues of this algebra over non-Archimedean local fields.

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