A mysterious duality: M-theory and del Pezzo surfaces

The discovery of duality symmetries in string theory has led to spectacular progress in our understanding of non-perturbative aspects of the theory. However, we still do not have a deep understanding of the meaning of these symmetries. Indeed, we find ourselves in the strange situation that the quantum corrected physics has more symmetries than the classical strings had any right to expect! It would be desirable to have a formulation of M-theory in which the U-duality symmetries were manifest. Here we will briefly describe a curious correspondence which may provide a hint about the ingredients of such a formulation.