Martin Winter (Max-Planck-Institute for Mathematics in the Sciences, Leipzig): Adjoint degrees and scissors congruence for polytopes

Abstract:
Hilbert’s Third Problem asks whether for any two (3-dimensional) polytopes there is a way to
cut the first one into finitely many pieces and rearrange them to obtain the second one (that is, we
ask whether the polytopes are “scissors congruent”). Its resolution by Max Dehn (with a negative
answer) marks the beginning of valuation theory, which to this day provides often one of the most
elegant approaches to problems in the geometric theory of polytopes. In this talk we take a look
at a particular valuation of recent interest - the canonical form - and we shall explore what it can
teach us about scissors congruence for polytopes. It will turn out that the degree of the so-called
adjoint polynomial is a fundamental parameter in this context. We investigate the polytope classes
defined by their adjoint degrees.
This is joined work with Tom Baumbach, Ansgar Freyer and Julian Weigert.
 

Before this lecture, starting at 4:45 p.m., there will be coffee and tea in Room 1404.

Everyone is cordially invited.

Signed: Prof. Dr. Torsten Mütze