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Solving puzzles of shellable simplicial spheres

Yirong Yang, University of Washington
Wednesday, February 21, 2024 - 4:10pm to 5:00pm
PDL C-401 and via Zoom Link:
Yirong Yang
Yirong Yang


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:
Meeting ID: 915 4733 5974