Isaac Harris, Ph.D. 


Assistant Professor
Purdue University 
150 N. University Street, West Lafayette, IN 47907
Office: MATH 612
Email: iharris1107[at]gmail.com - or - harri814[at]purdue.edu 

I graduated from The University of Delaware with a Ph.D. in Applied Mathematics under the advisement of Fioralba Cakoni in 2015. In August of 2018, I  joined the Department of Mathematics at Purdue University as an Assistant Professor. From Summer 2015-2018 I was at Texas A&M University as a Visiting Assistant Professor continuing my research in Inverse Problems and Scattering Theory with my mentor Bill Rundell

Here are links to my CV and Google Scholar page. 

Some Updates 

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Education

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Research 
My research interests are in direct and inverse problems for PDEs, especially those arising in acoustic and electromagnetic scattering. I have been working on the inverse scattering problem of non-destructive testing for defects in complex media and parameter identification for periodic media. My research employs techniques from a multitude of areas in mathematical analysis, such as Functional analysis, Analysis of PDEs, Numerical and Asymptotic methods. 

This figure is the cover image for Inverse Problems Volume 31 Number 2
Reconstructions of circular cavities in an Anisotropic material via the factorization method.

Research Interests: Direct and Inverse Scattering, Transmission Eigenvalue Problems, Inverse Problems for (Fractional) Diffusion, Qualitative Reconstruction Methods, Electrical Impedance Tomography, Inverse Spectral Problems, Homogenization, and Asymptotic Analysis 

Refereed Research Papers
  • I. Harris and A. Kleefeld "The inverse scattering problem for a conductive boundary condition and transmission eigenvalues". Applicable Analysis, DOI: 10.1080/00036811.2018.1504028  (arXiv:1608.07560)
  • F. Cakoni, I. Harris and S. Moskow "The Imaging of Small Perturbations in an Anisotropic Media".  Computers and Mathematics with Applications Volume 74, Issue 11, 2017 2769-2783 (arXiv:1702.06058)
  • L. Hoeltgen, I. Harris, A. Kleefeld and M. Breuss "Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian" Scale Space and Variational Methods in Computer Vision (2017), 66-79. Lecture Notes in Computer Science Volume 10302, Springer
  • I. Harris and S. Rome "Near field imaging of small isotropic and extended anisotropic scatterers".  Applicable Analysis Volume 96, No. 10, 2017 1713-1736 (arXiv:1601.02993)
  • O. Bondarenko I. Harris, and A. Kleefeld "The interior transmission eigenvalue problem for an inhomogeneous media with a conductive boundary". Applicable Analysis Volume 96, No. 1, 2017 2-22 (arXiv:1510.01762)
  • F. Cakoni, H. Haddar, and I. Harris "Homogenization of the transmission eigenvalue problem for periodic media and application to the inverse problem". Inverse Problems and Imaging Volume 9, No. 4, 2015, 1025–1049 (arXiv:1410.3729)
  • F. Cakoni and I. Harris "The factorization method for a defective region in an anisotropic material". Inverse Problems, 31 025002 (2015) (arXiv:1410.3737)
  • I. Harris, F. Cakoni, and J. Sun "Transmission eigenvalues and non-destructive testing of anisotropic magnetic materials with voids". Inverse Problems, 30 035016 (2014) (Preprint
Other Publications: 
  • I. Harris “Parameter identification for complex materials using Transmission Eigenvalues”. Oberwolfach Report, No. 45 (2016) 46-48. Extended Abstract for the workshop: Theory and Numerics of Inverse Scattering Problems
  • I. Harris "Non-Destructive Testing of Anisotropic Materials". The University of Delaware, Ph.D. Thesis (2015)
Papers in Preparation or Submitted: 
  • L. Hoeltgen, A. Kleefeld, I. Harris and M. Breuss "Theoretical Foundation of the Weighted Laplace Inpainting Problem" (Submitted) (arXiv:1801.09068)
  • I. Harris "Detecting an inclusion with a generalized impedance condition from electrostatic data via sampling" (Submitted) (arXiv:1708.03203)
  • I. Harris and W. Rundell "A direct method for reconstructing inclusions and boundary conditions from electrostatic data" (Under Preparation) (arXiv:1704.07479)
  • I. Harris and J. Rezac “Direct sampling algorithms for Spectral Density and Near-Field Acoustic Scattering”. (Under Preparation-Working Title) 
  • I. Harris and A. Kleefeld “Analysis of new direct sampling indicators for Far-field measurements”. (Under Preparation-Working Title) 
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Teaching Fall 2018
I am not teaching this Fall Semester!!!