For almost half a century, shell-model theory has served as a reference tool for the interpretation of nuclear spectroscopy. However, its impact was restricted at first by a limited knowledge of the effective Hamiltonian on the one hand and by the magnitude of the associated computations on the other hand. In the last decade, an improvement in our understanding of nuclear dynamics and the availability of ever growing computing power have radically changed the status of shell-model theory and have pushed it to the forefront among nuclear theoretical models. This article, which provides an introduction to the modern literature on the subject, offers many examples of its achievements, including an enhanced understanding of nuclei very far from stability.

Low-temperature reactive plasmas offer promise for assembling nanostructures in systems including silicon films, carbon nanotip arrays, and ceramic coatings. This Colloquium discusses the requirements for nanofabrication and the unique features of the reactive plasmas. In particular, the chemical processing of the plasma provides building blocks for the nanostructures that would not be otherwise available.

Quantum information theory often focuses on discrete states like those in qubits but states with continuous variables such as the coherent electromagnetic field of lasers can also be employed. This review discusses the theory of quantum information and entanglement for continuous variables, with application to quantum optical systems. Recent experimental developments include secure communication, teleportation of quantum states, and the demonstration of a quantum memory.

Long-range correlations, described by scale-invariant functions are commonly found on thermodynamic phase boundaries. Such behavior may also become generic, occurring within an entire phase. This article discusses how such generic correlations arise and influence the critical behavior at the transitions. Quantum phase transitions, in particular, are seen to be very susceptible to the effects of generic scale invariance.

Electromagnetically induced transparency is an example of controlling the propagation of electromagnetic fields by the coherent manipulation of resonances in the medium. Such control is now practical for gas-phase systems, giving media with radically new optical properties. This review treats the phenomena and underlying theory and discusses future prospects and potential applications.

String theory has had a major impact on a number of areas in pure mathematics, including knot theory and the geometry of Calabi-Yau manifolds. The author discusses the application of topological string theory in these areas, beginning with the classical work by Witten on the use of Chern-Simons theory to construct knot invariants.

The spectroscopies at terahertz, infrared, and optical frequencies have now provided a comprehensive picture of the low-energy excitations and charge dynamics in high-$T_c$ superconductors. This review is focused on the universal trends that are emerging from a large body of work by many research teams.