Intro -- Contents -- Preface -- Winding numbers for networks with weak angular data -- The snake charmer's algorithm -- Using a robot to learn geometric information from permutations of landmarks -- Geometric descriptions of polygon and chain spaces -- Diffusion over tensor fields via Lie group PDE flows: Lagrangian action approach -- Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles -- Symmetric Motion Planning -- Topological complexity of formal spaces -- Topological complexity of generic hyperplane complements -- Homotopy Meaningful Hybrid Model Structures -- Presentations for the cohomology rings of tree braid groups -- Competitive Disconnection Detection in On-Line Mobile Robot Navigation.