# Hailun Zheng: Techniques in constructing neighborly polytopes and spheres

**Time: **
Wed 2021-10-27 10.15 - 11.15

**Location: **
Zoom meeting ID: 654 5562 3260

**Participating: **
Hailun Zheng (University of Copenhagen)

Abstract: A simplicial polytope or a simplicial sphere on \(n\) vertices is \(k\)-neighborly if it has the same \((k-1)\)-skeleton as the \((n-1)\)-simplex. It is known that every simplicial \(d\)-polytope or \((d-1)\)-sphere on \(n\geq d+2\) vertices is at most \(\lfloor d/2\rfloor\)-neighborly. How many combinatorially distinct simplicial \(d\)-polytopes and \((d-1)\)-spheres on \(n\) vertices are there? What about the \(\lfloor d/2\rfloor\)-neighborly ones? In this talk, I will survey recent results on counting the combinatorial types of polytopes and spheres. Then I will present several techniques in constructing many neighborly polytopes and spheres. This is joint work with Isabella Novik.

Zoom meeting ID: 654 5562 3260

Zoom link: https://kth-se.zoom.us/j/65455623260

The seminar can also be viewed in room 3721.