Extremizers in Fenchel and Bezout-Type Inequalities

Explore a 31-minute lecture on extremizers in Fenchel and Bezout-type inequalities presented by Maud Szusterman at the Hausdorff Center for Mathematics. Delve into the study of affine invariant ratios involving mixed volumes, as investigated by Soprunov, Zvavitch, and Saroglou. Examine the characterization of the simplex as the unique minimizer for one of these ratios, and learn about the ongoing conjecture for a similar characterization of the smaller invariant. Discover how maximizers for the latter ratio correspond to equality cases in Fenchel inequality. Investigate the maximizers for the former ratio, including the cube but not the cross-polytope, and understand the open problem of identifying all maximizers in this context.