Balanced manifolds or how to decorate a pumpkin

The enumeration of faces of various types of simplicial complexes is a promnent topic in algebraic, topological and geometric combinatorics. In this talk, I will first provide a short survey on what is known for general simplicial complexes, simplicial polytopes and triangulations of manifolds. In the second part, the focus lies on balanced simplicial complexes, i.e., simplicial complexes whose underlying graph permits a minimal proper coloring in the graph-theoretic sense.