Matter can be detected by its gravitational pull. Many different observations together indicate that about 84% of the gravitating matter in the universe emits no detectable photons. This is the dark matter, and the quest to understand what it is drives the work of large communities in cosmology and particle physics. Experiments like the Large Underground Xenon experiment, LUX, are designed to search for possible interactions between dark matter particles and the particles of the Standard Model. Surveys like the Rubin Observatory Legacy Survey of Space and Time, LSST, will carefully map out the distribution of dark matter, probing for signs that some particle physics interactions was at work along with gravity and affected the evolution of structure. Gravitational wave observations may also reveal something about the nature of dark matter if, for example, the population of detected black holes is inconsistent with the expected astrophysical population.

Loop Quantum Gravity is a theory of quantum gravity based on a geometric formulation that predict discrete geometrical phenomena above some minimum length scale (the Planck length).

Physics often advances when crisp mathematical structures are uncovered in a framework developed to describe observed phenomena. For example, in quantum field theory there is a vast discrepancy between the current calculational difficulty in making predictions for experiments and the simple, mathematical form of the end result. The Amplitudes program seeks to explain and exploit this surprising simplicity by reformulating the basic mathematical tools used to make predictions.

Neutrinos are light, electrically-neutral elementary particles that make up the least-understood part of the Standard Model of particle physics. Facilities like DUNE (the Deep Underground Neutrino Experiment) study neutrinos produced in the Fermilab collider as well as neutrinos arriving from cosmic events. Project 8 will measure neutrino mass by looking at neutrinos emitted when tritium decays. The CMB Stage 4 telescopes will use cosmological data to constrain the number of neutrinos and their mass. Many other neutrino facilities focus on detecting neutrinos produced in astrophysical processes, including ANITA, ARA, BEACON, GRAND, IceCube, PUEO, and RNO-G. These cosmic neutrinos can carry key information, along with electromagnetic radiation and gravitational waves, in "multi-messenger" detections of dynamic events in the universe.

Physical mathematics is concerned with mathematics motivated by physics.

All physical systems obey the laws of quantum mechanics, but we have not yet achieved a full understanding of the relationship between quantum mechanics, general relativity, and cosmology. The primordial universe and black holes are two arenas to study these questions in ways that are complementary to research on laboratory quantum systems and quantum information.

The strong force out-competes the electromagnetic force on short distances to hold protons together in atomic nuclei. Nuclear matter can be studied in particle colliders and astrophysical objects like neutron stars. The quantum effects of particles that feel the strong force are important for many measurements in particle physics, including the recently measured anomalous magnetic moment of the muon. Many theoretical predictions of the effects of the strong force rely on the numerically-intensive work that requires supercomputers.