Pre-seminar is on Wednesday in Padelford C-401 at 3:30pm-3:55pm.

In the early 90's, Richard Stanley introduced the notion of local $h$-vectors in order to understand the behavior of the usual $h$-vector under subdividing a simplicial complex. In particular this allowed him to prove that the coordinates of the $h$-vector increase in nearly all cases. We will review the most common types of subdivisions and their relationships. We will then focus on results and open problems concerning possible characterizations of the local $h$-vector in each of these types.

This is joint work with Martina Juhnke-Kubitzke and Lukas Katthän.