Most of my publications are concerned with the hyperboloidal method, which is a technique to *follow light to infinity* using suitable coordinates for numerical computations. Originally motivated by gravitational waves, explorations of this technique led me to many other topics such as black hole perturbation theory, numerical methods, and PDE analysis.

- Devised a practical method that solves the
*outer boundary problem*and the*radiation extraction problem*in numerical calculations of wave equations [1]. - Introduced horizon-penetrating, hyperboloidal coordinates in black-hole perturbation theory [2], [3] and performed the first numerical computations with such coordinates [4], [5], [6].
- Computed the first global approximation of a black hole Green function in time domain (with Chad Galley) [7]. We explained the shape of caustic echoes from black holes by an optical effect discovered in 1890.
- Computed the first gravitational waves at null infinity on the background of a rotating black hole (with Gaurav Khanna). We demonstrated an efficiency gain of at least 5000 in one simulation [8].
- Contributed to the Simulating-eXtreme-Spacetimes Collaboration. Two papers from that collaboration [9], [10] have been cited by the first detection of gravitational waves that led to the 2017 Nobel Prize in Physics.

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