Łukasz P. Michalak: Vertex-minimal triangulations of spaces with a given fundamental group

Given a finitely presented group $G$ we consider the problem of finding the minimum number $n$ such that there is a simplicial complex $K$ on $n$ vertices with $\pi_1(K) \cong G$. During the talk we will present some asymptotic results, as well as some approaches to the classification of fundamental groups of complexes with a small number of vertices.