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DTSTART;TZID=America/Toronto:20250324T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-signe-lundqvist
SUMMARY:Algebraic Graph Theory-Signe Lundqvist
CLASS:PUBLIC
DESCRIPTION:TITLE: Euclidean and projective rigidity of hypergraphs\n\nSPE
 AKER:\n\nSigne Lundqvist\n\nAFFILIATION:\n\nUmeå University\n\nLOCATION:\
 n Please contact Sabrina Lato for Zoom link.\n\nABSTRACT: The mathematic
 al theory of structural rigidity has a long\nhistory. In the nineteenth ce
 ntury\, Cauchy studied rigidity of\npolyhedra\, and Maxwell studied graph 
 frameworks. The rigidity theory\nof graph frameworks has since been studie
 d extensively.\nPollaczek-Geiringer\, and later Laman\, proved a combinato
 rial\ncharacterization of the minimally rigid graphs in the plane.\n\nComb
 inatorial rigidity theory is also concerned with geometric\nrealizations o
 f other combinatorial structures. In this talk\, we will\nfocus on rigidit
 y of realizations of hypergraphs as points and\nstraight lines. We will di
 scuss how to determine whether a realization\nof a hypergraph is rigid\, i
 n the sense that there are no motions of\nthe realization that preserve th
 e incidences of points and lines\, and\nthe distance between any pair of p
 oints that lie on a line.\n\nWe will also discuss motions of realizations 
 of hypergraphs that\npreserve only the incidences between points and lines
 . We will see\nthat classical theorems in incidence geometry\, such as Pas
 cal's\ntheorem\, make determining rigidity with respect to such motions a\
 ndifficult problem.\n\nThe talk will be based on joint work with K.Stokes 
 and L-D. Öhman\, as\nwell as work in progress\, joint with L.Berman\, B.S
 chulze\, B.Servatius\,\nH.Servatius\, K.Stokes and W.Whiteley.
DTSTAMP:20260403T081852Z
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