Binary Scalar Products

Explore a 23-minute lecture on binary scalar products presented by Stephan Weltge from the Hausdorff Center for Mathematics. Delve into the resolution of a conjecture proposed by Bohn, Faenza, Fiorini, Fisikopoulos, Macchia, and Pashkovich in 2015 regarding 2-level polytopes. Learn about the unique property of these polytopes, where for every facet-defining hyperplane H, there exists a parallel hyperplane H0 such that both H and H0 contain all vertices. Discover the proof of the conjecture, which states that for any d-dimensional 2-level polytope P, the product of its number of vertices and number of facets is at most d2^(d+1). Gain insights into this important mathematical concept and its implications in the field of geometry and polytope theory.