Explore the fascinating world of minimal triangulations in manifolds through this 47-minute lecture on fundamental groups of small simplicial complexes. Delve into the computation of fundamental groups for simplicial complexes with up to 8 vertices and discover how these calculations contribute to new estimates for vertex counts in minimal triangulations of manifolds. Learn about the classification, reduction, and main procedures involved in this complex mathematical topic. Gain insights into the challenges and open problems in the field of applied algebraic topology as presented by Dejan Govc from the Applied Algebraic Topology Network.