ACT I - Invitation to Geometry via Mahler's Conjectures: a mathematical opera in three acts

Act I: Convexity, Duality, and Volume

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

This will be lecture 1 of 3. Please see additional information about lecture 2 here, and lecture 3 here.

You can learn more about Professor Yanir Rubinstein here: https://math.umd.edu/~yanir/