Guillermo Pineda Villavicencio gave a seminar at TU Berlin on the 17th of September.
Title: Lower bound theorems on the face numbers of polytopes with few vertices
Abstract: We study lower bound theorems for the number of $k$-faces ($1\le k\le d-2$) of a $d$-dimensional polytope $P$ (or \emph{$d$-polytope}) with up to $3d-1$ vertices. Earlier results include the following: Xue (2021) established the case of polytopes with at most $2d$ vertices; Xue (2022) and Pineda-Villavicencio and Yost (2022) independently settled the case of $2d+1$ vertices; and Pineda-Villavicencio, Tritama, and Yost (2024) extended this to $2d+2$ vertices.