Please Note: This seminar will be given in person.
Randomized Petty projection inequality
Affine isoperimetric inequalities concern with functionals on classes of convex bodies in which ellipsoids play an extremal role. A fundamental example is the Petty projection inequality which states that among all convex bodies of the same volume, ellipsoids maximize the volume of polar projection bodies.
In this talk, we establish empirical versions of the Petty projection inequality and its generalizations. This provides a random extension of the Petty projection inequality which can be derived by the law of large numbers.
Joint work with G. Paouris and P. Pivovarov.