BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ryoshun Oba (University of Tokyo) DTSTART:20200723T140000Z DTEND:20200723T150000Z DTSTAMP:20260423T052641Z UID:VSAMRT/11 DESCRIPTION:Title: Characterizing the Universal Rigidity of Generic Tensegrities\nby Ryos hun Oba (University of Tokyo) as part of Virtual seminar on algebraic matr oids and rigidity theory\n\n\nAbstract\nA tensegrity is a structure made f rom cables\, struts and stiff bars. A d-dimensional tensegirty is universa lly rigid if it is rigid in any dimension d′ with d′≥d. The celebrat ed super stability condition due to Connelly gives a sufficient condition for a tensegrity to be universally rigid. Gortler and Thurston showed that super stability characterizes universal rigidity when the point configura tion is generic and every member is a stiff bar. We extend this result in two directions. We first show that a generic universally rigid tensegrity is super stable. We then extend it to tensegrities with point group symmet ry\, and show that this characterization still holds as long as a tensegri ty is generic modulo symmetry. Our strategy is based on the block-diagonal ization technique for symmetric semidefinite programming problems\, and ou r proof relies on the theory of real irreducible representation of finite groups.\n LOCATION:https://researchseminars.org/talk/VSAMRT/11/ END:VEVENT END:VCALENDAR