|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 non-overlapping 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 k-th rational homology of the ordered configuration space of n points on a connected non-compact 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.
Speaker: Nick Wawrykow
Event Organizer: Jennifer Wilson email@example.com