Multiplicative structure on valuations and its analogues over local fields.

Abstract: Valuation on convex sets is a classical notion of convex geometry. Multiplicative structure on translation invariant smooth valuations was introduced by the speaker years ago. Since then several non-trivial properties of it have been discovered as well as a few applications to integral geometry. In the first part of the talk we will review some of these properties. Then we discuss analogues of the algebra of even translation invariant valuations over other locally compact (e.g. complex, p-adic) fields. While any interpretation of these new algebras is missing at the moment, their properties seem (to the speaker) to be non-trivial and having some intrinsic beauty.

analysis of PDEsmetric geometry

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

If you are interested in giving a talk, please let one of the organizers know. Also, please suggest speakers which you would like to hear talk. Most talks are 50 minutes, but some 20-minute talks will be paired up as well. The talks will be video recorded conditioned upon the speakers' agreement.