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

# On polynomially integrable convex bodies

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

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.