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Configuration Spaces of Graphs

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The configuration space of a finite number of particles in a topological space is an object of interest in many areas of mathematics, in particular if the ambient space is a manifold. While the geometry of configuration spaces of manifolds is understood quite well, the case of particles in general simplicial complexes remains rather mysterious, even for 1-dimensional complexes. In this talk, I will describe an efficient combinatorial model for configurations of particles in a finite graph, which was first defined by Jacek Światkowski. Afterwards, I will sketch the other techniques we used to prove torsion-freeness and representation stability of those configuration spaces’ homology.

This talk is part of the Junior Geometry Seminar series.

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