I am a postdoctoral researcher in gravitational waves at the Albert Einstein Institute in Potsdam. My current research interests are in black hole perturbation theory and deep-learning methods for data analysis.

I grew up in Toronto, Canada, where I attended the University of Toronto. I obtained my PhD in physics at the University of Chicago under Robert Wald, where I studied effects of general relativity in cosmology and debunked the idea that small scale structure could drive cosmological acceleration and mimic dark energy. I then moved to the University of Guelph and Perimeter Institute, where I studied turbulence in gravitational waves and black hole superradiant instabilities. Now I am a member of LIGO, and my work focuses on gravitational waves.

- Gravitational Waves
- Black Holes
- Deep Learning

PhD in Physics, 2012

University of Chicago

SM in Physical Sciences, 2006

University of Chicago

BSc in Mathematics and Physics, 2005

University of Toronto

Use normalizing flows for Bayesian inference of system parameters from gravitational-wave detector data.

Develop new methods for nonlinear perturbations of the Kerr spacetime and make predictions for extreme mass-ratio inspirals for LISA.

When can fields extract mass from black holes and drive instabilities? What is the endpoint?

What happens when gravitational waves are confined by spacetime geometry so that nonlinear interactions take hold? What is the end point of the AdS instability?

Can cumulative relativistic effects of small scale structure mimic Dark Energy?

The LIGO and Virgo gravitational-wave observatories have detected many exciting events over the past five years. As the rate of detections grows with detector sensitivity, this poses a growing computational challenge for data analysis. With this in mind, in this work we apply deep learning techniques to perform fast likelihood-free Bayesian inference for gravitational waves. We train a neural-network conditional density estimator to model posterior probability distributions over the full 15-dimensional space of binary black hole system parameters, given detector strain data from multiple detectors. We use the method of normalizing flows—specifically, a *neural spline* normalizing flow—which allows for rapid sampling and density estimation. Training the network is likelihood-free, requiring samples from the data generative process, but no likelihood evaluations. Through training, the network learns a *global* set of posteriors: it can generate thousands of independent posterior samples per second for any strain data consistent with the prior and detector noise characteristics used for training. By training with the detector noise power spectral density estimated at the time of GW150914, and conditioning on the event strain data, we use the neural network to generate accurate posterior samples consistent with analyses using conventional sampling techniques.

We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in a Teukolsky framework. We first show that solutions to the linearized Einstein equation with nonvanishing stress tensor can be decomposed into a pure gauge part plus a zero mode (infinitesimal perturbation of the mass and spin) plus a perturbation arising from a certain scalar (“Debye-Hertz”) potential, plus a so-called “corrector tensor.” The scalar potential is a solution to the spin $-2$ Teukolsky equation with a source. This source, as well as the tetrad components of the corrector tensor, are obtained by solving certain decoupled ordinary differential equations involving the stress tensor. As we show, solving these ordinary differential equations reduces simply to integrations in the coordinate $r$ in outgoing Kerr-Newman coordinates, so in this sense, the problem is reduced to the Teukolsky equation with source, which can be treated by a separation of variables ansatz. Since higher order perturbations are subject to a linearized Einstein equation with a stress tensor obtained from the lower order perturbations, our method also applies iteratively to the higher order metric perturbations, and could thus be used to analyze the nonlinear coupling of perturbations in the near-extremal Kerr spacetime, where weakly turbulent behavior has been conjectured to occur. Our method could also be applied to the study of perturbations generated by a pointlike body traveling on a timelike geodesic in Kerr, which is relevant to the extreme mass ratio inspiral problem.