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The number of realizations of a Laman graph

Matteo Gallet
Institution: 
SISSA
Location: 
A-137
Schedule: 
Tuesday, January 21, 2020 - 15:00
Abstract: 

Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. Such realizations can be seen as solutions of systems of quadratic equations prescribing the distances between pairs of points. Using ideas from algebraic and tropical geometry, we provide a recursive formula for the number of complex solutions of such systems.This is a joint work with Jose Capco, Georg Grasegger, Christoph Koutschan, Niels Lubbes, and Josef Schicho.

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