Large Structures Seminar: Louis Theran

This talk is part of the AScI Thematic program "Challenges in Large Geometric Structures and Big Data" seminar. Check out our upcomning talks at https://aaltoscienceinst.github.io/lsbdseminar/.

Where:	AScI lounge (TUAS 3161)
When:	08.03.2016 @ 16.15

Speaker:	Louis Theran Aalto University
Title:	GORs, stresses, and generic universal rigidity

A graph $G$ is generically globally rigid (GGR) in dimension $d$ if, for a generic bar-joint framework $(G,p)$ any other $d$ -dimensional framework $(G,q)$ with the same edge lengths is related to $(G,p)$ by a Euclidean motion. A stronger notion is that of universal rigidity, in which $(G,q)$ may be in any dimension $D\ge d$ . Universal rigidity is known not a to be generic property, but we can show that for any GGR graph, there are open sets of universally rigid frameworks. This answers a question of Gortler and Thurston.

The approach is to analyze a construction of Alfakih that relates so-called “super stable” configurations to orthogonal representations of graphs introduced by Lovász, Saks and Schrijver.

This is joint work with Bob Connelly and Shlomo Gortler.