Pulsars are rapidly rotating, highly magnetized neutron stars which emit a beam of radiation along their magnetic field axis. The misalignment of their magnetic field axis with their rotational axis is why we call them pulsars - as the star swings its radiation beam into our line-of-sight we register a brief pulse of electromagnetic radiation in our detectors. Hence, these pulsars are nature's lighthouses.
A particular breed of pulsars spin around hundreds of times per second. These millisecond pulsars (MSPs) have such stable and predictable pulse arrival times that we can use them as natural clocks in the sky. We build up highly accurate models for these pulse arrival times, then dig into any small deviations of the real arrival times from our predictions. It is in these deviations (or "residuals") that may lie some fascinating prospects for gravitational-wave detection.
A background of nanohertz gravitational waves will bathe all the pulsars in our galaxy with its common influence. This background jiggles the Earth and pulsars up and down, much like buoys on the surface of an ocean, causing advances or delays in the pulsar arrival times. If we look for structure in the timing residuals of a pulsar, and find significant power at nanohertz frequencies, then we might have a clue that a background of gravitational waves has left its mark.
However sometimes the pulsars themselves can create this structure. The only way we can unambiguously say that gravitational waves have affected the pulse arrival times is by observing many pulsars, then correlating the arrival times of the entire ensemble to look for common low-frequency structure. Such a background of gravitational waves could be produced by the inspiral of many supermassive black-hole binaries at the centers of recently merged galaxies all throughout cosmic time. If any of these signals is loud enough then we may be able to detect it as an individual source. See the options below for further details.
I have developed a codebase to perform Bayesian pulsar-timing inference (parameter estimation and model-selection), which can search for or provide limits on various determinstic or stochastic gravitational-wave signals influencing the times of arrival of radio pulses from pulsars.
I have developed a suite of techniques to probe the angular power distribution of the nanohertz GW sky. More recently, my collaborators and I adapted methods from CMB polarization studies to produce phase-coherent mapping strategies for the GW sky in the LIGO and PTA bands. This allows us to recover the gradient and curl modes of a GW background signal.
To truly understand the progenitor populations and evolutionary paths of compact binary systems, we need full population synthesis simulations under a wide range of parameter variations. I have developed a partial emulator of the full binary demographics that is trained on a restricted number of detailed simulations.