Yiran Wang
Emory University, GA·Mathematics & Statistics
Astronomers observe effects, such as light patterns, neutrinos and gravitational waves, and must work backward to their causes. This is an inverse problem.
- Fields
Mathematics & Statistics
Physics
Astronomy & Astrophysics
- Topics
inverse problems
cosmic microwave background
general relativity
- Grants
- 1 known grant, through Jul 2028
What they work on
- Recover the initial state of the Universe from the cosmic microwave background by combining an X-ray tomography approach with Einstein's equations, developing statistical inference and numerical reconstruction algorithms.
- Establish mathematical properties of geodesic ray transforms, which add up quantities along light paths, in Lorentzian and pseudo-Riemannian geometry, and address related rigidity questions.
- Determine how black hole quasinormal modes, the 'ringing' seen in gravitational-wave signals, relate to black hole parameters.
- Study scattering and inverse scattering on black hole spacetimes, including the high-energy stability and distribution of phase shifts.
More about the research
Solving one rigorously requires knowing whether the data determine the answer uniquely, how sensitive the answer is to errors in the data, and how to compute it efficiently. This mathematics project studies such inverse problems in cosmology and general relativity, Einstein's theory of gravity, and it has links to medical imaging.
Why it matters
This is basic mathematical research. It provides rigorous tools for working backward from telescope and gravitational-wave data to the early Universe and to black hole properties, which could help interpret future observations and scattering experiments. The same reconstruction mathematics may also inform medical imaging.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Francois Monard
University of California-Santa Cruz, CA·Mathematics & Statistics
Unify three complex-analytic methods for X-ray transforms, including transport twistor space, to derive exact reconstruction formulas in curved (Riemannian and non-Euclidean) geometries.
Peter Hintz
Pennsylvania State University, PA·Mathematics & Statistics
Prove nonlinear stability of Kerr black holes, the standard model of a rotating black hole, for all spins below the maximum, showing that small disturbances decay over time, using geometric and microlocal analysis of wave equations.
Lee Lindblom
University of California-San Diego, CA·Physics
Develop a way to determine the neutron-star equation of state, the pressure–density relationship of matter inside neutron stars, from observations and strong-gravity theory, without assuming any particular microphysics of that matter.
The school
Emory University: 70 labs on PI Pages, $1.2B a year on research, 286 research doctorates a year.
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