תאריך:
ה', 26/10/202314:30-15:30
מיקום:
Manchester Building (Hall 2), Hebrew University Jerusalem
Title: Isoperimetry and slices of convex sets
Abstract: The slicing problem by Bourgain is an innocent-looking question in convex geometry. It asks whether any convex body of volume one in an n-dimensional Euclidean space admits a hyperplane section whose (n-1)-dimensional volume is at least some universal constant. There are several equivalent formulations and implications of this conjecture, which occupies a rather central role in the field. The slicing conjecture would follow from the isoperimetric conjecture of Kannan, Lovasz and Simonovits, which suggests that the most efficient way to partition a convex body into two parts of equal volume so as to minimize their interface, is a hyperplane bisection, up to a universal constant. In this lecture we will discuss progress from the last two years, showing that these two conjectures hold true up to factors that increase logarithmically with the dimension.
Abstract: The slicing problem by Bourgain is an innocent-looking question in convex geometry. It asks whether any convex body of volume one in an n-dimensional Euclidean space admits a hyperplane section whose (n-1)-dimensional volume is at least some universal constant. There are several equivalent formulations and implications of this conjecture, which occupies a rather central role in the field. The slicing conjecture would follow from the isoperimetric conjecture of Kannan, Lovasz and Simonovits, which suggests that the most efficient way to partition a convex body into two parts of equal volume so as to minimize their interface, is a hyperplane bisection, up to a universal constant. In this lecture we will discuss progress from the last two years, showing that these two conjectures hold true up to factors that increase logarithmically with the dimension.