Continuing innovations in integrated circuit miniaturization and low-power local networking have made feasible the vision of distributed computers consisting of numerous cheap processing elements with limited local connectivity. Motivating practical examples of such systems include environmental sensor networks, cell phones, and multi-agent robotics. One pressing problem is how to perform system-wide analysis, assembling local information to infer or actuate global results. Recent advances have leveraged local-to-global principles from algebraic topology to provide robust algorithms for engineering systems. These include 1) homological methods for sensor networks, 2) topological complexity for robot motion planning, 3) simplicial complexes for planning in the presence of uncertainty, and 4) sheaf theory for network data aggregation and optimization.
This workshop will focus attention on the best and newest topological tools for applications in robotics, sensor networks, communications networks, signal processing, and more. The workshop will provide an excellent opportunity for curious researchers from diverse backgrounds to learn new mathematics or new applications. The goal of the workshop is to exchange ideas, problems, techniques, and motivations.