Speaker: Ileana Streinu
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Title: Points in motion
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In this talk, I will present some very recent results on kinetic point
sets, defined as points moving with constant speeds along linear
trajectories, and kinetic graphs, defined as graphs embedded on kinetic
point sets. The problems of interest include collision prediction, and
maintaining non-crossing properties or other geometric embedding features
such as edge directions.
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The results include a combinatorial characterization of the collision
events for kinetic point sets. This is done by relating them to a refined
(oriented matroidal) oriented-projective view of configuration spaces
(parallel redrawings) of certain types of direction newtorks (graphs with
additional slope information associated to their edges) with good rigidity
theoretic properties (independent in the rigidity matroid).  Collisions in
kinetic point sets are captured via rigid components in an associated
direction network. Non-crossing kinetic graphs with parallel redrawings
appear - surprisingly - as collapsed pointed pseudo-triangulation
mechanisms.