**SMS scnews item created by Haotian Wu at Thu 17 May 2018 1741**

Type: Seminar

Distribution: World

Expiry: 16 Nov 2018

**Calendar1: 24 May 2018 1200-1300**

**CalLoc1: Carslaw 351**

CalTitle1: Geometry & Topology Seminar: Yaskin -- On polynomially integrable convex bodies

Auth: haotianw@dora.maths.usyd.edu.au

### Geometry & Topology Seminar

# On polynomially integrable convex bodies

### Vlad Yaskin (University of Alberta)

**Thursday 24 May 12:00–13:00 in Carslaw 351.**

Please join us for lunch after the talk!

**Abstract:**
Let \(K\) be a convex body in \(\mathbb R^n\). The parallel section function of \(K\) in the direction \(\xi\in S^{n-1}\) is defined by \(A_{K,\xi}(t)=\mathrm{vol}_{n-1}(K\cap \{\langle x,\xi\rangle =t\}), \; t\in \mathbb R\). \(K\) is called polynomially integrable (of degree \(N\)) if its parallel section function in every direction is a polynomial of degree \(N\). We prove that the only convex bodies with this property in odd dimensions are ellipsoids. This is in contrast with the case of even dimensions, where such bodies do not exist, as shown by Agranovsky. This is a joint work with A. Koldobsky and A. Merkurjev.