Graph braid group are the fundamental groups of configuration spaces of particles in a graph. Topological complexity is the measure of discontinuity of the motion planning problem. In this talk I will discuss those notions. I will also describe a nonpositively curved cube complex associated to each graph braid group and how it can be used to compute its topological complexity. This is joint work with Kevin Schreve.
Kasia Jankiewcz will be joining the Mathematics Department as a new assistant professor this summer, after spending the 2024-2025 academic year at the Institute for Advanced Study. Prior to that she was an L.E. Dickson Instructor at the University of Chicago (2018-2021) before moving to a faculty position at University of California, Santa Cruz, where she was awarded an NSF CAREER grant.