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Session II.3 - Real-Number Complexity

Friday, June 16, 14:30 ~ 15:00

The zonoid algebra and random intersections in symmetric spaces

Peter Bürgisser

TU Berlin, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We assign to a compact symmetric space $M$ a commutative graded algebra, whose elements are certain convex bodies (zonoids) in the exterior algebra of the cotangent space $V$ of $M$. They can be viewed equivalently as measures on the Grassmann manifolds of $V$. This Grassmann zonoid algebra allows to describe the intersection of randomly moved submanifolds of $M$, much like the cohomology algebra of $M$ describes intersections with sign count. Moreover, the link to convexity enforces inequalities in the style of the Alexandrov Fenchel inequality. There is a close connection to the theory of valuations.

Joint work with Paul Breiding (University of Osnabrück), Antonio Lerario (SISSA) and Leo Mathis (University of Frankfurt).

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