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"Mathematical Problems in Cosmological X-ray Tomography"

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Friday, February 25, 2022, 1 pm– 2 pm

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Cosmic Microwave Background (CMB) is the radiation remnant from the Big Bang and is considered as a primary source of information regarding the early universe. From the work of Sachs and Wolfe (1967), it is known that one can extract an X-ray transform (called the light ray transform) of the early gravitational perturbations by considering the linearization of the CMB anisotropies. We discuss recent results about the transform and the inverse problem of recovering gravitational perturbations. We explain the essential ingredient in the analysis which is the microlocal property of the light ray transform and its interplay with hyperbolic type PDEs. Also, we explore the transport equation theory for the light ray transform and discuss the application to inverse source problems for the Boltzmann equation in the CMB kinetic theory as well as some nonlinear problems in Nordstrom’s scalar gravitation theory.


Dr. Yiran Wang is an Assistant Professor at the Department of Mathematics, Emory University. Before that, he was a Postdoc Scholar at Stanford University working with Prof. András Vasy. He also worked with Prof. Gunther Uhlmann as an Acting Assistant Professor at the University of Washington with a joint position at IAS, HKUST. He obtained his Ph.D. degree from Purdue University under the supervision of Prof. Antônio Sá Barreto. His research interests are microlocal analysis, inverse problems, integral geometry, spectral, and scattering theory.

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