# Antonio Lerario: The zonoid algebra

**Time: **
Tue 2022-10-04 10.15

**Location: **
3721, Lindstedtsvägen 25, and Zoom

**Video link: **
Meeting ID: 621 8808 6001

**Participating: **
Antonio Lerario (KTH and SISSA)

### Abstract

In this seminar I will discuss the so called "zonoid algebra", a construction introduced in a recent work (joint with Breiding, Bürgisser and Mathis) which allows to put a ring structure on the set of zonoids (i.e. Hausdorff limits of Minkowski sums of segments). This framework gives a new perspective on classical objects in convex geometry, and it allows to introduce new functionals on zonoids, in particular generalizing the notion of mixed volume. Moreover this algebra plays the role of a probabilistic intersection ring for compact homogeneous spaces. Joint work with P. Breiding, P. Bürgisser and L. Mathis