Workshop on Topology: Identifying Order in Complex Systems

This will be a report on topics related to topological complexity (TC), introduced by Michael Farber in 2003 as a numerical measure of the complexity of robot motion planning problems. TC of real projective space P^n (lines through the origin in Euclidean n+1 space) coincides with the Euclidean immersion dimension of P^n for n different from 1, 3 and 7. For symmetric TC of P^n , there is a close relation to the Euclidean embedding dimension of P^n , currently under study. Joint work with Jesus Gonzalez.