Abstract: This talk will discuss inverse problems in the photoacoustic imaging of two-photon absorption of heterogeneous media, where we intend to reconstruct coefficients in systems of semilinear diffusion and transport equations from single or multiple given data sets. We will present technical results, but our goal is really to give an overview of recent developments on the modeling, computational and mathematical aspects of the problem.
Short bio: Kui Ren received his PhD in applied mathematics from Columbia University. He then spent a year at the University of Chicago as an L. E. Dickson instructor before moving to University of Texas at Austin to become an assistant professor in mathematics. He returned to Columbia University in 2018 as a professor in applied mathematics. Kui Ren's recent research interests include inverse problems, mathematical imaging, random graphs, fast algorithms, kinetic modeling, and computational learning.
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