Isabella Novik - Face Numbers - The Upper Bound Side of the Story
Explore the fascinating world of face numbers in simplicial polytopes and triangulations of spheres in this 47-minute lecture by Isabella Novik. Delve into the upper bound problem, examining the maximum number of i-dimensional faces in various geometric structures. Investigate the properties of cyclic polytopes, simplicial complexes, and the Upper Bound Theorems. Compare the abundance of spheres to polytopes and analyze the proportion of neighborly polytopes. Examine centrally symmetric polytopes and spheres, exploring their unique properties and limitations. Discover recent developments in the field, including the existence of certain structures and open problems. Gain insights into this captivating area of mathematics through a comprehensive survey of known results and ongoing research questions.