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Type cones and products of simplices

Bennet Goeckner, University of Washington
Wednesday, April 7, 2021 - 3:30pm to 5:00pm
via Zoom

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting:
Meeting ID: 915 4733 5974

A polytope \$P\$ is the convex hull of finitely many points in Euclidean space. For polytopes \$P\$ and \$Q\$, we say that \$Q\$ is a Minkowski summand of \$P\$ if there exists some polytope \$R\$ such that \$Q+R=P\$. The type cone of \$P\$ encodes all of the (weak) Minkowski summands of P. In general, combinatorially isomorphic polytopes can have non-isomorphic type cones. We will first consider type cones of polygons, and then show that if \$P\$ is combinatorially isomorphic to a product of simplices, then the type cone is simplicial. This is joint work with Federico Castillo, Joseph Doolittle, Michael Ross, and Li Ying.