Act I: Convexity, Duality, and Volume
Act II: Convex meets Differential
Act III: Convex meets Complex
Once convexity, duality and volume appear on stage, the Mahler
Conjectures are inevitable. These conjectures, originating in Number Theory,
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, and their profound impact
on modern Geometric and Functional Analysis.