I graduated from The University of Delaware with a Ph.D. in Applied Mathematics under the advisement of Fioralba Cakoni in August 2015. I am currently at Texas A&M University where I am 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. In August of 2018 I will be joining the Department of Mathematics at Purdue University as an Assistant Professor.

- Referee, for the Journal of Computational Physics as of Febuary 2018
- Referee, for Communications in Mathematical Sciences as of August 2017
- Referee, for Inverse Problems as of August 2017
- Referee, for the Journal of Computers and Mathematics with Applications as of June 2017
- Referee, for the SIAM Journal on Imaging Science as of November 2016
- Referee, for the Journal of Computational and Applied Mathematics as of July 2016
- Referee, for the SIAM Journal on Mathematical Analysis as of January 2016
- Invited to the Theory and Numerics of Inverse Scattering Problems Workshop at Oberwolfach in Sept 2016 I was invited as a United States Junior Oberwolfach Fellow (slides)
- Invited Talk at the Post-Doc Seminar, IMA Minneapolis MN, December 2016
- Invited Mini-Symposium Spreaker at the SIAM CSE Conference in Atlanta GA, Febuary/March 2017 I recieved the NSF-SIAM Early Career Travel Award to attend the meeting (slides)
- Talk at the Texas DE Conference at TAMU, March 2017 (slides).
- Invited Spreaker at the University of Houston's PDE Seminar, April 7th 2017 (slides)
- Invited Mini-Symposium Spreaker at Applied Inverse Problems, Hangzhou China, May/June 2017
- Invited Mini-Symposium Spreaker at the SIAM Annual Meeting, Pittsburgh PA, July 2017
- I am giving a talk in the PDE Seminar at the University of Houston - Math Dept. (slides)
- I am giving a Special Colloquium talk at Purdue University - Math Dept. (slides)
- Invited AMS Special Section Spreaker at the Joint Math Meeting, San Diego CA, January 2018
- Invited Special Section Spreaker at the SIAM Annual Meeting, Portland OR, July 2018

- B.A. in Mathematics, Kean University, 2010
- M.S. in Applied Mathematics, University of Delaware, 2012
- Ph.D. in Applied Mathematics, University of Delaware, 2015 My Dissertaion is tittled "Non-Destructive Testing of Anisotropic Materials".

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.

**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

- F. Cakoni, I. Harris and S. Moskow "The Imaging of Small Perturbations in an Anisotropic Media".
- L. Hoeltgen, I. Harris, A. Kleefeld and M. Breuss "Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian"
- I. Harris and S. Rome "Near field imaging of small isotropic and extended anisotropic scatterers".
- O. Bondarenko I. Harris, and A. Kleefeld "The interior transmission eigenvalue problem for an inhomogeneous media with a conductive boundary".
- F. Cakoni, H. Haddar, and I. Harris "Homogenization of the transmission eigenvalue problem for periodic media and application to the inverse problem".
- F. Cakoni and I. Harris "The factorization method for a defective region in an anisotropic material".
- I. Harris, F. Cakoni, and J. Sun "Transmission eigenvalues and non-destructive testing of anisotropic magnetic materials with voids".
- I. Harris “Parameter identification for complex materials using Transmission Eigenvalues”.
- I. Harris "Non-Destructive Testing of Anisotropic Materials". University of Delaware, Ph.D. Thesis (2015)
- I. Harris "Detecting an inclusion with a generalized impedance condition from electrostatic data via sampling" (Submitted) (arXiv:1708.03203)
- I. Harris and A. Kleefeld "The inverse scattering problem for a conductive boundary condition and transmission eigenvalues". (Submitted) (arXiv:1608.07560)
- L. Hoeltgen, A. Kleefeld, I. Harris and M. Breuss "Theoretical Foundation of the Weighted Laplace Inpainting Problem" (Submitted) (arXiv:1801.09068)
- 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 W. Rundell "Recovering sources from time trace measurements for the (fractional) heat equation" (Under Preparation-Working Title)
- I. Harris "The direct and inverse problem for the fractional heat equation in a domain with an impedance subregion" (Under Preparation-Working Title)

**Research Papers in Refereed Journals: **

**Other Publications: **

**Papers in Preparation or Submitted:**

I am teaching MATH 308-Differential Equations at TAMU Section 518

Math 308 Syllabus.

Math Department course schedule. This course may not follow schedule exactly. Here is the PDF for the departments help session schedule, 308 will be MWTh from 7:00-10:00pm in Bloc 148.

Class Description/Learning Objectives: Ordinary differential equations, solutions in series, solutions using Laplace transforms, systems of differential equations. Basic hand computational techniques are still covered in this course, but perhaps not with the same emphasis as in the past. Students should be shown how to solve differential equations using the computer (both symbolically and numerically) and be expected to solve a modeling or applications problem/project where the computer is needed to complete the solution.

Homework 1 on Linear, Seperable and Exact 1st order equations.

Solutions to Quiz 1 on Linear, Seperable and Exact 1st order equations.

Homework 2 on the Uniqueness Theorems and Autonomous Equations. (Solu)

Solutions to Quiz 2 on Autonomous 1st order equations and the Uniqueness Theorem.

Homework 3 on the Linear Independance, Homogeneous 2nd order equations. (Solu)

Homework 4 2nd order equations continued with Reduction of order, Undetermined coefficents. (Solu - 2b correction)

Solutions to Quiz 3 on Linear Independance, 2nd order homogeneous equ's with constant coeff.

Exam 1 Topics: (Solu)

-1st order equ's: Linear, Separable and Exact

-2nd order equ's: Homogeneous with constant coefficient and Reduction of order

-Initial and Boundary Value problems

-Filtration Problems

Homework 5 on Undetermined coefficents and Variation of Parameters. (Solu)

Solutions to Quiz 4 on Undetermined Coefficents.

Homework 6 on Variation of Parameters and the definition of the Laplace Transform. (Solu)

The first MATLAB (Extra Credit) assignment is due 3/21 to replace lowest quiz grade.

Here is a table of basic Laplace Tranforms.

Homework 7 on the Laplace Transform for IVPs. (Solu)

Solutions to Quiz 5 on Variation of Parameters.

Homework 8 on the convolution Theorm for the Laplace Transform and BVPs. (Solu)

Homework 9 on the Piecewise continuous and Impulse functions. (Solu)

Solutions to Quiz 6 on the Laplace Transform for IVPs.

Exam 2 Topics: (Solu)

-2nd order nonhomogeneous equ's: Variation of parameters and Undetermined coefficients

-Laplace Transform: Solving IVPs/BVps, Piecewise continuous functions, Impulse Functions and Convolutions/Integral equ's

Solutions to Quiz 7 on the The Convolution Theorem.

Solutions to Quiz 8 on the Laplace Transform for Piecewise continuous and Impulse functions.

Homework 10 on Power series solutions and Euler's equation. (Solu)

THE (COMPREHENSIVE) FINAL WILL BE ON FRIDAY MAY 4TH AT 3:30-5:30 pm Blocker 133.

Last Updated: 4/19/18