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CATEGORIES:Combinatorics and Probability Seminar
SUMMARY:Rigidity of graphs - Anthony Nixon\, Lancaster
DTSTART:20221013T140000Z
DTEND:20221013T150000Z
UID:TALK5005AT
URL:/talk/index/5005
DESCRIPTION:A (bar-joint) framework is the combination of a gr
aph G and a map p assigning positions in Euclidean
d-space to the vertices of G. The vertices are mo
delled as universal joints and the edges as stiff
bars. The framework is rigid if the only edge-leng
th-preserving continuous deformation of the vertic
es arises from an isometry of the space. While it
is computationally difficult to determine if a giv
en framework is rigid\, the generic behaviour depe
nds only on the graph. Indeed\, when d=1\, G is ri
gid if and only if it is connected\, and when d=2\
, a precise combinatorial description was obtained
by Polaczek-Geiringer in the 1920s. However\, giv
ing a combinatorial description in all higher dime
nsions remains open 100 years later. The talk will
survey graph rigidity and then report on recent j
oint work on a particular special case as well as
an application to maximum likelihood estimation.
LOCATION:LTC
CONTACT:Johannes Carmesin
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