The main thrust of our unified description brings together the study of cosmological matter (black holes, dark matter/dark energy) on the scale of the Universe with the study of quantum matter (superconductors/superfluids, ultracold atomic gases) on the scale of the laboratory. Although the grand challenges at each length scale are altogether different, the mathematical methods can be developed in parallel, with analogues and dualities that are both insightful and useful. A prominent example is the use of string theory, originally developed for black holes, to describe electrons in a superconductor.
The research program of the D-ITP is based on three themes: cosmological matter, quantum matter, and topological matter. For each theme, a compact set of challenges is described and parallel methods are identified. These methods emphasize the unity of theoretical physics, and at the same time allow us to introduce novel mathematical concepts and techniques in adjacent fields.
Our ambition for each of the three themes is to use advanced mathematical methods to make essential contributions towards the resolution of outstanding problems on the nature and structure of matter. The list of open problems includes some long-term challenges at the Nobel level (e.g., the origin of gravity and dark matter, the mechanism of high-temperature superconductivity), but also a diverse collection of shorter-term challenges (e.g., the classification of topological insulators, the use of Majorana fermions for quantum computing).