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URL:/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-signe-lundqvist
SUMMARY:Algebraic Graph Theory-Signe Lundqvist
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Euclidean and projective rigidity of hyperg
 raphs\n\nSPEAKER:\n\nSigne Lundqvist\n\nAFFILIATION:\n\nUmeå University\n
 \nLOCATION:\n Please contact Sabrina Lato for Zoom link.\n\nABSTRACT: Th
 e mathematical theory of structural rigidity has a long\nhistory. In the n
 ineteenth century\, Cauchy studied rigidity of\npolyhedra\, and Maxwell st
 udied graph frameworks. The rigidity theory\nof graph frameworks has since
  been studied extensively.\nPollaczek-Geiringer\, and later Laman\, proved
  a combinatorial\ncharacterization of the minimally rigid graphs in the pl
 ane.\n\nCombinatorial rigidity theory is also concerned with geometric\nre
 alizations of other combinatorial structures. In this talk\, we will\nfocu
 s on rigidity of realizations of hypergraphs as points and\nstraight lines
 . We will discuss how to determine whether a realization\nof a hypergraph 
 is rigid\, in the sense that there are no motions of\nthe realization that
  preserve the incidences of points and lines\, and\nthe distance between a
 ny pair of points that lie on a line.\n\nWe will also discuss motions of r
 ealizations of hypergraphs that\npreserve only the incidences between poin
 ts and lines. We will see\nthat classical theorems in incidence geometry\,
  such as Pascal's\ntheorem\, make determining rigidity with respect to suc
 h motions a\ndifficult problem.\n\nThe talk will be based on joint work wi
 th K.Stokes and L-D. Öhman\, as\nwell as work in progress\, joint with L.
 Berman\, B.Schulze\, B.Servatius\,\nH.Servatius\, K.Stokes and W.Whiteley.
 \n 
DTSTAMP:20250711T115748Z
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