DMS Topology Seminar

Speaker: Hannah Albert 

Title: Homology of configuration spaces of squares in a rectangle

Abstract: We consider the configuration space of n unit squares sliding in a p by q rectangle.  In which degrees is its homology concentrated?  Squares in a rectangle serve as a model for molecules in a container.  Can we detect (approximately) whether the substance is a solid, liquid, or gas, using only the topology of the configuration space?  Even very basic questions about these configuration spaces tend to be unresolved, so there are many appealing directions for future research.