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Geometry-Topology Seminar

Thursday, October 8, 2020 - 4:30pm

Andrew Cooper

UPenn

Location

University of Pennsylvania

via Zoom

The Zoom link is: https://upenn.zoom.us/j/91890239234 This same Zoom link will apply for future talks as well. It is set to open at 4 PM so that speakers can come on early and check out their technology setups. The talks will begin at 4:30 PM. We will also stay afterwards, say from 5:30 - 6 PM to chat with one another, as an online substitute for going out to dinner with our speakers. We encourage everyone to have a nice bottle of wine at hand for that social half hour. For further information about the seminar, please contact Mona Merling (mmerling@math.upenn.edu), Davi Maximo (dmaxim@math.upenn.edu) or Herman Gluck (gluck@math.upenn.edu).

 
Given a space X, the configuration space of n points on X is the space of ways to distribute those points in X without allowing any pair to coincide.
 
But what if we allow some subsets of the points to coincide? The allowed coincidences form a simplicial complex S; we call the resulting simplicial configuration space X_S. In many ways the theory of simplicial configuration spaces generalizes the theory of configuration spaces, but is richer because of the combinatorial structure S.
 
I will discuss some tools for computing the homology of X_S, as it reflects the topology of X and combinatorial properties of S. Along the way, we'll discover a novel polynomial invariant of simplicial complexes which generalizes the chromatic polynomial of graphs.
 
Time permitting, I will also mention a few ideas for applying this structure to social choice problems ranging from romantic comedy to the descent into war.