Abstract:
This talk focuses on shellable simplicial spheres, which are triangulations of topological spheres with a special combinatorial decomposition property. I will describe recent progress on two fundamental questions: how many shellable spheres exist, and how much information is encoded in their facet-ridge graphs. For the first question, I will briefly go over Nevo, Santos, and Wilson’s construction of many odd-dimensional simplicial spheres and sketch why they are shellable, thereby obtaining an asymptotic result. For the second question, I will outline how to recover the full combinatorial structure of a shellable sphere from its facet-ridge graph. I will conclude with nice examples of shellable spheres arising as independence complexes of Gorenstein planar ternary graphs.
Note: There will be no pre-seminar. The main talk starts at 4:10.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974