Topology Seminar

The combinatorics and representation stability of orbit configurations spaces

Nir Gadish, Massachusetts Institute of Technology

Friday, October 23rd, 2020
2:00 PM - 3:00 PM
Zoom ID 677 596 7436

Given a space X with a group action one may consider the space of n-tuples of points in X belonging to distinct orbits - the so called orbit configuration space. These natural generalizations of the ordinary configuration spaces arise e.g. as covers of configuration spaces, and also as complements of arrangements associated with root systems. Studying the topology of these spaces from a combinatorial point of view leads to a new class of posets, which are particularly interesting when the group action is not free. In this talk I will describe this combinatorial approach. We will see in particular how a recursive structure of the relevant posets leads to good control over the topology. An efficient way to organize the resulting structure proceeds by collecting the orbit configuration spaces of all cardinalities into a certain algebra object, which is then showed to exhibit a kind of representation stability. This work is joint with Christin Bibby.‚Äč

Event contact: steven dot amelotte at rochester dot edu