### Some remarks on Mahler's conjecture for convex bodies

Zvavitch, A *(Kent State University)*

Wednesday 16 February 2011, 14:00-15:00

Seminar Room 1, Newton Institute

#### Abstract

Let $P(K)$ be the product of the volume of an origin symmetric convex body $K$ and its dual/polar body $K^*$. Mahler conjectured that $P(K)$ is minimized by a cube and maximized by a ball. The second claim of this conjecture was proved by Santalo; despite many important partial results, the first problem is still open in dimensions 3 and higher. In this talk we will discuss some recent progress
and ideas concerning this conjecture.

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