Surprising Representations in Cohomology of Configurations in Graphs

Explore the mathematical intricacies of configuration spaces in graphs during this Special Year Seminar II lecture by Nir Gadish from the University of Pennsylvania. Delve into the nonsmooth analogs of braid arrangements that appear in robotics applications and moduli spaces of tropical curves. Learn about the challenging nature of understanding their cohomology, which depends on the underlying graph's combinatorics, while discovering how their one-point compactification serves as a fascinating homotopy invariant. Examine the mysteriously familiar representations of the symmetric group appearing in their cohomology, understand their origins, and discover their connections to the cohomology of moduli spaces of tropical curves. The seminar takes place on April 17, 2025, at 10:00am in Simonyi 101 at the Institute for Advanced Study.