TL;DR
This paper surveys the current state of the volume product problem in convex geometry, highlighting key estimates and recent progress, based on the author's previous work and conference presentation.
Contribution
It provides an overview of the latest upper and lower bounds for the volume product problem, summarizing recent advances in the field.
Findings
Summarizes known upper and lower bounds for the volume product.
Highlights recent progress and key estimates in the problem.
Provides an overview based on the author's prior research and conference talk.
Abstract
In this small survey we consider the volume product, and sketch some of the best upper and lower estimates known up to now, based on our paper [BMMR]. The author thanks the organizers of the conference in Jurata, March 2010, for their kind invitation, and the excellent atmosphere there. This paper is based on the talk of the author on that conference.
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