Seminar by Kateryna Tatarko

Monday, March 27, 2023 4:00 pm - 4:00 pm EDT (GMT -04:00)

Please Note: This seminar will be given in person.

Probability seminar series 

Kateryna Tatarko
University of Waterloo

Room: M3 3127

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.