Special Colloquium
Hailun Zheng
University of Houston-Downtown
The problem of polytope reconstruction
Abstract: What partial information about a convex $d$-polytope is enough to uniquely determine its combinatorial type? This problem, known as the problem of polytope reconstruction, has been extensively studied since the sixties. For instance, a famous result of Perles asserts that simplicial $d$-polytopes are determined by their $\lfloor d/2 \rfloor$-skeletons.
In this talk, I will survey recent advances in this field, from mainly two perspectives. 1) realizability: can a certain simplicial complex be realized as the ($\lfloor d/2 \rfloor-1$)-skeleton of a simplicial $d$-polytope or a simplicial $(d-1)$-sphere? 2) sufficiency: can the $i$-skeleton (where $i < \lfloor d/2 \rfloor$), together with some additional information such as affine $(i+1)$-stresses, determine the combinatorial or even affine type of the polytope?
This is joint work with Satoshi Murai and Isabella Novik
Wednesday February 22, 2023 at 3:00 PM in 636 SEO