Josh Hinman, University of Washington
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PDL C-401 and via Zoom Link: https://washington.zoom.us/j/91547335974
Abstract:
We generalize a result about the face numbers of polytopes to the realm of CW spheres. Let X be a CW sphere such that:
- X is strongly regular. (The intersection of any two faces is a face.)
- X is shellable. (We can build X, facet by facet, so that each facet intersects with the previous ones in a predictable way.)
Then X is a "squishy polytope", resembling a polytope topologically and combinatorially but not geometrically. We prove a set of linear lower bounds on the face numbers of X in terms of the number of facets. To do so, we translate an argument about solid angles into an argument about shellings.
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: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974