# Betti numbers of colored simplicial complexes

**Time: **
Wed 2019-03-27 10.15 - 11.00

**Lecturer: **
Afshin Goodarzi

**Location: ** Room 3418, Lindstedtsvägen 25. Department of Mathematics, KTH

Abstract: A simplicial complex is r-colored if its 1-skeleton is r-colorable in the graph theoretic sense. In this talk, we describe the convex hull of the set of Betti vectors of r-colored complexes on n vertices. We show that this polytope is a simplex whose vertices are Betti vectors of skeleta of the clique complex of Turán’s graph T(n, r). This resolves a conjecture of Kozlov (1997).