geometers are interested in the problem of finding a "best"
metric on a manifold. in dimension 2, the best metric is usually one
which possesses the most symmetries, such as the round metric on a
sphere, or a flat metric on a torus. in higher dimensions, there are
many more classes of geometrically interesting metrics. i will give a
general overview of a certain class of einstein metrics in dimension 4
which have special holonomy, and which are known as "gravitational
instantons." i will then discuss certain aspects of their classification
and connections with algebraic surfaces.