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In this talk, we discuss a new regularized version of the Factorization Method. The Factorization Method uses Picard's Criteria to define an indicator function to image an unknown region. In most applications, the data operator is compact which gives that the singular values can tend to zero rapidly which can cause numerical instabilities. The regularization of the Factorization Method presented here seeks to avoid the numerical instabilities in applying Picard's Criteria. This method allows one to image the interior structure of an object with little a priori information in a computationally simple and analytically rigorous way. Here we will focus on an application of this method to diffuse optical tomography which will prove that this method can be used to re-cover an unknown subregion from the Dirichlet-to-Neumann mapping.
A native of New Jersey, Professor Harris was a McNair and LSAMP scholar at Kean University, where he graduated with honors in 2010. He received his Ph.D. in Applied Mathematics at the University of Delaware under the direction of Fioralba Cakoni in 2015. During his time as a graduate student, he also spent a summer at the Ecole Polytechnique in Palaiseau, France, where he studied transmission eigenvalues and their relationship to estimating a scatterers material properties. From 2015 to 2018 Professor Harris was a Postdoctoral Visiting Professor at Texas A&M University. In the fall of 2018, he joined the Department of Mathematics as a new tenure-track assistant professor at Purdue University.