Stochastic methods in dual Brunn--Minkowski theory

Speaker(s)

Peter Pivovarov

Affiliation

Univeristy of Missouri

Language of the talk

English

Date

Nov. 7, 2024, 12:15 p.m.

Room

room 3160

Title in Polish

Stochastic methods in dual Brunn--Minkowski theory

Seminar

Seminar of Probability Group

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The surface area of a convex body can be obtained as an average of the areas of its shadows (1-codimensional projections).  In turn, the surface area is just one of the k-quermassintegrals of a convex body, which involve averaging areas of projections on k-dimensional subspaces.  These quantities occupy a central role within Brunn--Minkowski theory and satisfy a number of extremal inequalities, which include the standard isoperimetric theorem.  In the class of convex sets, projections and sections are dual notions. However, there are striking parallel inequalities for sections that extend well outside of the class of convex sets, notably within Lutwak’s Dual Brunn—Minkowski theory. I will describe a stochastic approach to deriving some of these dual inequalities for sections. Based on joint work with G. Paouris and P. Simanjuntak.

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