Sequential topological complexity and sectional categories of subgroup inclusions

The sequential topological complexities (TCs) of a space are integer-valued homotopy invariants that are motivated by the motion planning problem from robotics. After outlining their definitions, I will discuss the sequential TCs of aspherical spaces and describe how they can be investigated by purely algebraic means. Sectional categories of subgroup inclusions are straightforward generalizations of this algebraic setting and we will discuss how to obtain lower bounds on their values using elementary homological algebra and discuss consequences for sequential TCs. This is joint work with Arturo Espinosa Baro, Michael Farber and John Oprea.