# Jan-Marten Brunink: Combinatorics of antiprism triangulations

**Time: **
Wed 2020-12-09 10.15 - 11.15

**Lecturer: **
Jan-Marten Brunink

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

Abstract: The antiprism triangulation gives a natural way to subdivide a simplicial complex \(\Delta\), similar to the barycentric subdivision. It can be defined as the simplicial complex of chains of multi-pointed faces of \(\Delta\), from a combinatorial point of view, and by successively applying crossing operations on faces of \(\Delta\), from a geometric point of view. In this talk we review enumerative invariants and algebraic properties of this triangulation, such as the \(h \)-vector transformation of a simplicial complex \(\Delta\) under antiprism triangulation. In particular we show, that the \(\Delta\)-polynomial of the antiprism triangulation of a simplex is real-rooted and that for every shellable complex \(\Delta\) the antiprism triangulation of \(\Delta\) has the almost strong Lefschetz property over \(\mathbb{R}\). This is joint work with Christos Athanasiadis and Martina Juhnke-Kubitzke.

Zoom meeting ID: 654 5562 3260