Department of Mathematics

Consider n points evolving within a convex polygon according to one of the following interaction laws: (i) each point moves away from the closest other point or polygon boundary, (ii) each point moves toward the furthest vertex of its own Voronoi polygon, or (iii) each point moves toward a geometric center (centroid, circumcenter, incenter, etc) of its own Voronoi polygon. These interaction laws give rise to strikingly simple dynamical systems whose behavior remains largely unknown. Which are their critical points? What is their asymptotic behavior? Are they optimizing any aggregate function? In what way do these local interactions give rise to distributed systems? Are they of any engineering use in robotic coordination problems? In this talk, we'll try to answer some of these questions.