Topology Seminar: Hannah Alpert

Take n objects and put them in a container. What is the configuration space of all the ways they can fit in the container without intersecting? How does the topology of that configuration space change depending on the size of the objects and the size of the container? We will look at configurations of segments in a disk, of squares in a rectangle, and of disks in an infinite strip. In the latter two cases, the configuration space is homotopy equivalent to a polyhedral cell complex that can be studied combinatorially.