Mathematicians from Europe and the US discuss geometry, algebraic geometry, and topology, including the basic properties of uniformly rational varieties, new relations between algebraic topology and the theory of Hopf, a measured foliated 2-complex thin type, the classical geometry of complexes, a generalization of the amoeba and the Ronkin function of a

plane algebraic curve for a pair of harmonic functions, and natural differential-geometric constructions on the algebra of densities.

As an intermediate step towards the third result, we also show that for a fixed family of

plane algebraic curves with s degrees of freedom, every set of n points in the plane has a subset of [OMEGA]([n.