Date: Friday, February 04, 2022
Location: 1866 East Hall (4:00 PM to 4:50 PM)
Title: Configuration spaces and secondary representation stability
Abstract: An ordered configuration space is the space of ways of putting labeled nonoverlapping objects (points, disks, etc.) in another space (manifold, graph, etc.). Church, Ellenberg, and Farb and later Miller and Wilson proved that the sequence consisting of the kth rational homology of the ordered configuration space of n points on a connected noncompact manifold of dimension at least 2 exhibits a type of stability, namely once you have at least n=2k points, this sequence stabilizes as a sequence of symmetric group representations. This is first order representation stability. Miller and Wilson proved that the unstable homology classes satisfy a notion of "secondary representation stability," that arises from adding a pair of orbiting points "near infinity". We will discuss their results, introducing the category FIM^+ and the arc resolution spectral sequence.
Files:
Speaker: Nick Wawrykow
Institution: UM
Event Organizer: Jennifer Wilson jchw@umich.edu
