The relations between the covering number \tau(F) and the fractional covering number \tau^*(F) of a hypergraph F play a role in various combinatorial problems. We discuss the following result: If the (hereditary) homological dimension of the nerve of F is bounded by d then \tau(F) < c_1 \tau^*(F)^{c_2} where c_1,c_2 depend on d alone. We will describe the connections to the fractional Helly property together with some applications to geometrical piercing problems.

This talk does not require prior knowledge of homology theory. The relevant background will be presented in the talk.

This is joint work with Noga Alon, Gil Kalai and Jiri Matousek.