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Explore the parametrized approach to motion planning in this 51-minute lecture from the Applied Algebraic Topology Network. Delve into the concept of fiber bundles, where the base space parametrizes external constraints on the system. Examine how input (initial and terminal states) and output (a path between them) of a motion planning algorithm must adhere to the same external conditions within a fiber of the bundle. Investigate the parametrized motion planning problem specifically for spaces that are complements of hyperplane unions in complex vector spaces. Learn about the determination of parametrized topological complexity for fiber bundles of arrangement complements under the combinatorial hypothesis of supersolvability. Gain insights from joint work with Dan Cohen in this advanced exploration of algebraic topology and motion planning.
