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URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences
 -department-colloquium-eran-nevo-hebrew-university-jerusalem
SUMMARY:Mathematical Sciences Department Colloquium: Eran Nevo, Hebrew Univ
 ersity of Jerusalem
DESCRIPTION:Mathematical Sciences Colloquium\nEran Nevo, The Hebrew Univers
 ity of Jerusalem\nFriday, September 11\n11:00 am\nStratton 202\n\nTitle: R
 igidity, expansion and polytopes\nAbstract: Given a graph G and an embeddi
 ng of its vertices in R^d, what continuous motions of the vertices preserv
 e all edge lengths? Clearly all motions induced by an isometry of R^d do, 
 these are the trivial motions; are there any others? If the answer is NO f
 or all (equivalently, for one) generic embedding, G is called d-rigid. Wha
 t are the d-rigid graphs?\nThis problem has been extensively studied since
  the 70s, and is still widely open for d≥3. It is studied mainly from alge
 braic geometry and combinatorial points of view. Variants of it, especiall
 y in dimensions 2 and 3, are of importance also beyond mathematics, e.g. i
 n structural engineering, computational biology and more.\nI will focus on
  a quantitative version of rigidity via spectral analysis of the related s
 tiffness matrix, including the construction of “rigidity expanders”, gener
 alizing expandergraphs. This area of research is still a mostly uncharted 
 territory, and I'll present various directions for future study along the 
 way.Time permitting, higher dimensional notions of rigidity and of stiffne
 ss matrices, and their relation to the study of polytopes, will be address
 ed.\n
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