Bergman Lectures: Invitation to Geometry via Mahler's Conjectures: a mathematical opera in three acts

Abstract: Once convexity, duality and volume appear on stage, the Mahler Conjectures are inevitable. These conjectures predict the extremizers of the volume of a convex body times the volume of its dual. They date from the 1930's and are still largely open.

This ``mathematical opera" mostly aimed at a broad mathematical audience will attempt to recount the over-a-century-old story of these beautiful conjectures.

Act I:   Convexity, Duality, and Volume

Act II:  Convex meets Differential

Act III: Convex meets Complex