At the dawn of gravitational-wave astronomy, there is renewed focus on the range of astrophysical sources and the information that can be extracted from observations. This one-week workshop motivated new theoretical work on continuous gravitational-wave sources and improved the communication between nuclear physicists, gravitational-wave experts, and astrophysicists working on dense matter and compact objects.

Key issues discussed at the workshop included:

1. The modeling of solid material phases at extreme densities. The gravitational radiation from a spinning compact object is very sensitive to its shape, and solids keep their shape. Therefore, gravitational waves provide a unique probe of astrophysical solids including neutron star crust, nuclear pasta, and possible high-density solid phases of QCD.

2. Constraints on the gravitational-wave emission from electromagnetic observations, e.g. of accreting stars, and a discussion of the most promising astrophysical scenarios for targeted gravitational-wave searches.

3. The design of theory-led search strategies, including constraints from electromagnetic observations.

• Introduction to gravitational waves for nuclear physicists.
• Introduction to nuclear physics and dense matter for gravitational-wave physicists.
• Continuous gravitational-wave searches.
• Crust mountains and mountain building.
• R-modes.
• Neutron star crust and crust properties.
• Magnetic and compositional mountains.
• Superfluid dynamics and neutron star oscillations.
• Crust strength and crust breaking.
• Magnetar giant flares, and GW bursts.
• Dense QCD and solid phases at high density.

The workshop identified a number of areas for further work. The shear modulus and breaking strain of nuclear pasta should be explored. These complex phases could make up half of the mass of the crust of neutron stars. The configuration, strength, and stability of toroidal magnetic field components should also be studied. These fields, if very strong, could produce important deformations.

Continuous gravitational wave searches with Advanced LIGO and Advanced VIRGO may soon reach three important milestones. First, observations of accreting sources may probe spin equilibrium where the accretion torque spinning up a star is balanced by a spin down torque from gravitational wave radiation. Second, gravitational wave observations of the Crab pulsar may become sensitive to deformations of a size that can be supported by the crust. These observations will then be sensitive to violent formation processes for this young and active star that left an imprint in the shape of the crust. Finally, searches may soon beat the spin down limit for a millisecond pulsar. One will then be sensitive to smaller "residual" deformations that could be present on many stars.