Isoperimetric inequalities in high-dimensional convex sets
Bo'az Klartag, Joseph Lehec
TL;DR
This paper discusses recent advances in understanding the geometric properties of high-dimensional convex sets, focusing on isoperimetric inequalities related to the Bourgain slicing problem and the KLS conjecture.
Contribution
It provides an overview of recent progress and techniques addressing key open problems in high-dimensional convex geometry.
Findings
Progress towards Bourgain's slicing problem
Advances on the KLS isoperimetric conjecture
New techniques in high-dimensional convex analysis
Abstract
These are lecture notes focusing on recent progress towards Bourgain's slicing problem and the isoperimetric conjecture proposed by Kannan, Lovasz and Simonovits (KLS).
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Taxonomy
TopicsPoint processes and geometric inequalities · Limits and Structures in Graph Theory · Graph theory and applications