UW Combinatorics and Geometry Seminar: 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.