Professor Kastner's group is studying the motion of electrons in nanometer-size semiconductor structures and in transition-metal oxides. These are systems in which the motion of electrons is highly correlated. In simple metals and semiconductors, like Aluminum and Silicon, each electron moves as though it were independent of all the others. The Coulomb interactions of the other electrons creates an average potential that changes things like the electron's effective mass, but for the most part, a single-electron picture is adequate. In the oxides of transition metals, this single-particle model breaks down. The electrons are highly localized in the atomic orbitals of the transition metal ions and, as a result, the motion of each electron strongly affects the motion of others. This results in unusual magnetic and electronic properties. In the case of the transition metal oxides, this localization takes place naturally. However, in the past few decades, the techniques developed for the electronics industry have allowed us to create artificially localized electrons, which also display strong correlations. One example is the single electron transistor. This is a device in which electrostatic fields confine electrons to a small region of space inside a semiconductor. The confinement causes the number of electrons in the small region to be quantized, and other effects of strong correlations, such as the Kondo effect, can be observed. While one confined droplet of electrons can be studied in a single electron transistor, it is also interesting to study arrays of confined regions. Kastner's group is doing this in collaboration with Prof. Moungi Bawendi's Group of the MIT Department of Chemistry. In this case, the system consists of arrays of identical nano-crystals grown by a colloidal chemistry technique.