Department of Mathematics and Statistics at the Faculty of Science
University of Calgary
Rigidity of polytopes, areas of polygons, and the Robbins conjectures
Submitted by ppaterso on Wed, 02/11/2009 - 12:52pm.
Feb 13 2009 - 12:00pm
Feb 13 2009 - 1:00pm
Speaker:
Igor Pak (Dept. of Math., University of Minnesota )
Location:
MS 431Discrete Geometry Seminar
Some of the most classical mathematical questions ask about
the volumes of polytopes
given the edge lengths. In 1995, David Robbins published a series of conjectures on what he called
the generalized Heron polynomials, giving the area of inscribed polygons. All these conjectures were
recently proved using a mixture of tools from combinatorics and algebraic geometry. In this talk,
I will survey this work and spend much of my time outlining a deep connection with therigidity of convex
polytopes and the bellows conjecture on the volume of flexible polytopes (resolved by Sabitov).
given the edge lengths. In 1995, David Robbins published a series of conjectures on what he called
the generalized Heron polynomials, giving the area of inscribed polygons. All these conjectures were
recently proved using a mixture of tools from combinatorics and algebraic geometry. In this talk,
I will survey this work and spend much of my time outlining a deep connection with therigidity of convex
polytopes and the bellows conjecture on the volume of flexible polytopes (resolved by Sabitov).