Solving puzzles of shellable simplicial spheres

Abstract:

Reconstructing simplicial complexes from partial information has been a problem of interest for decades. A triangulation of a $d$-dimensional sphere is obtained by gluing a collection of $d$-dimensional simplices (“higher dimensional triangles”) along their faces, such that the resulting simplicial complex is homeomorphic to a topological $d$-sphere. For such a triangulation, if we only know the number of simplices in the triangulation and which pairs of simplices are glued along a $(d-1)$-face, can we uniquely recover the entire combinatorial structure of the triangulation? In this talk, I will show the answer is yes for shellable spheres, generalizing the result from the 1980s on reconstructing simple polytopes from their 1-skeleta.

Note: There will be no pre-seminar this week. The talk will start at 4:10.

Join Zoom Meeting: https://washington.zoom.us/j/91547335974
Meeting ID: 915 4733 5974