American Institute of Mathematics, Palo Alto, California
Alexander Koldobsky, Vladyslav Yaskin, and Artem Zvavitch
We propose to bring together leading experts in the area and young researchers to discuss further development of the Fourier approach to sections of convex bodies, with focus on uniqueness problems, stability and hyperplane inequalities. We are going to start by collecting results and open problems on determination of convex bodies by volumes of certain classes of hyperplane sections. In the cases where convex bodies are uniquely determined by this data, we ask the corresponding volume comparison problem, namely if volumes of all sections from a certain class are smaller for one body than for another, is it true that the volume of the first body is also smaller. If the answer to a volume comparison problem is affirmative, we ask a stronger stability question and, if possible, apply stability to derive hyperplane inequalities in the spirit of the Hyperplane Conjecture, one of the most important open problems in convex geometry.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Vertex index of symmetric convex bodies by Litvak
`Convexity' of Intersection Bodies by Kim
GEOMETRIC TOMOGRAPHY: Sections of Convex (and Star!) Bodies by Gardner