The Goldhaber-Gordon group uses advanced fabrication techniques to confine electrons to semiconductor nanostructures, to extend our understanding of quantum mechanics to interacting particles -- when constrained this way, electrons cannot easily avoid each other -- and to provide the basic science that will shape possible designs for future transistors. The Goldhaber-Gordon group makes precision electrical measurements and designs novel scanning probe techniques that allow direct spatial mapping of electron organization and flow. For some of their measurements of exotic quantum states, they cool electrons to a hundredth of a degree above absolute zero, among the coldest temperatures ever achieved for semiconductor nanostructures. They also work to elucidate behavior of related materials such as magnetic topological insulators and graphene, a single atomic layer of carbon atoms.