Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 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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