Shape Recognition of Convex Bodies

Speaker: Sergii Myroshnychenko University of Alberta

Date: Wed, Nov 4, 2020

Location: PIMS, University of British Columbia, Zoom

Conference: Emergent Research: The PIMS Postdoctoral Fellow Seminar

Subject: Mathematics

Class: Scientific

Abstract:

A broad class of convex geometry problems deals with questions on retrieval of information about (convex) sets from data about different types of their projections, sections, or both. Examples of such assumptions are volume estimates, rigidity of structure, symmetry conditions etc.

In this talk, we will discuss known results and recent developments regarding the dual notions of point-projections and non-central sections of convex bodies. In particular, we provide a partial affirmative answer to the question on a shape recognition posed by A. Kurusa, and discuss a generalization of V. Klee's theorem for polyhedra.