Title: On the length of knots on a Heegaard surface of a 3-manifold. Abstract: In this talk we explore connections between the topology and the geometry of 3-manifolds. Concretely, we use Heegaard-splittings (topology) of a 3-manifold to describe hyperbolic structures (geometry) on it. More concretely, for a knot K that lies on a Heegaard surface F of a closed oriented connected 3-manifold M, we describe a sufficient condition for M to carry a hyperbolic structure. The sufficient condition is in terms of topological information about the triple (M,F,K). Furthermore, whenever our criterion applies, we provide bounds on the length of K. The upshot is that there is no Ricci-flow machine running in the background. Instead, the motor behind what we do is effective hyperbolic Dehn surgery ala Hodgson and Kerckhoff. This talk is based on work in progress with A. Sisto and G. Viaggi.