Joseph Doolittle: Counterexamples to Perles Conjecture

Abstract: A recurring question about polytopes is how much information is required to fully determine the polytope. The first interesting answer to this is Steintz's 1922 theorem that the graph of a 3-polytope determines the polytope. The graph of a simple polytope determines the polytope. In 1970, Perles conjectured that the facets of simple polytopes could be read from the graph by checking certain reasonable conditions. Haase and Ziegler gave a counterexample to this conjecture in 2002. Building upon their work, we find many counterexamples, and disprove even the weakest possible version of Perles conjecture. In this talk, we discuss the constructions and tools used, and explore how these may be used to study a conjecture of Kalai on simplicial spheres.

Zoom meeting ID: 695 4578 9922