**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/ 91547335974Meeting ID: 915 4733 5974**