Safia Chettih

CDH 105
1100 NE Campus Pkwy, Seattle, WA 98105
Given a general graph, we can construct discretized models for its npoint configuration space that are cubical complexes. The model constructed by A. Abrams in his 2000 PhD thesis is the most wellknown, but in 2001 Świątkowski constructed a lesserknown model whose dimension stabilizes as the number of points increases. In recent work with Daniel Lütgehetmann, we have considered a Świątkowskistyle discretized model for configurations with sinks, where multiple points are allowed to occupy certain vertices of the graph. In my talk, I will discuss these various constructions and sketch the techniques we used to prove torsionfreeness and representation stability for the homology of configurations on trees with loops.