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SUMMARY:Boulos El Hilany (TU Braunschweig)
DTSTART:20221117T151500Z
DTEND:20221117T170000Z
DTSTAMP:20260422T070001Z
UID:CJCS/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/88/">Co
 upler curves of moving graphs and counting realizations of rigid graphs</a
 >\nby Boulos El Hilany (TU Braunschweig) as part of Copenhagen-Jerusalem C
 ombinatorics Seminar\n\n\nAbstract\nA calligraph is a graph that for almos
 t all edge length assignments moves with one degree of freedom in the plan
 e\, if we fix an edge and consider the vertices as revolute joints. \nThe 
 trajectory of a distinguished vertex of the calligraph is called its coupl
 er curve. Each calligraph corresponds to an algebraic series of real curve
 s in the plane. I will present a description for the class of those curves
  in the Néron-Severi lattice of the plane blown-up at six complex conjuga
 te points. \n\nA graph is said to be minimally rigid if\, up to rotations 
 and translations\, admits finitely many\,\nbut at least two\, realizations
  into the plane for almost all edge length assignments. \nA minimally rigi
 d graph can be expressed as a union of two calligraphs\, and the number of
  its \nrealizations is equal to the product of classes of those two callig
 raphs. I will show how one \ncan apply those observations to produce an im
 proved algorithm that counts the numbers of realizations. \nThis\, in turn
 \, allows one to characterize invariants of coupler curves.\n\nThis is a j
 oint work with Georg Grasegger and Niels Lubbes (Symbolic computation grou
 p\, RICAM\, Austria)\n
LOCATION:https://researchseminars.org/talk/CJCS/88/
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