Abstracts
for the Seminar

Fall 2018

**Speaker: **Michael Dobbins, Binghamton University

**Title: **Grassmannians and Pseudosphere Arrangements

**Time:** 2:30 PM, Monday, September 10, 2018

**Place:** Malott 206

**Abstract:**In this talk I will present a metric space of pseudosphere arrangements, as in the topological representation theorem of oriented matroids, where each pseudosphere is assigned a weight. This gives extensions of the spaces of full rank vector configurations that have nicer combinatorial and topological properties. In rank 3, these
spaces modulo SO(3) are homotopy equivalent to Grassmannians, and for any fixed oriented matroid, the subspace of representations of that oriented matroid is contractible. This was partly motivated by combinatorial tools for working with vector bundles.

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