Postdoctoral Research Associate

Department of Mathematics

University of North Carolina at Chapel Hill

120 E Cameron Avenue, Chapel Hill, NC 27599

Office: Phillips 303

Email: ggranad [at] unc.edu

Recent Updates

• Will present at the SIAM Central States Section Annual Meeting, Fayetteville AR (Invited, October 2025)

• Presented at The Third Joint SIAM/CAIMS Annual Meetings, Montréal CAN (Invited, July 2025)

• Presented in the SoMSS Seminar, Arizona State University (Invited, May 2025)

• Presented at the SIAM Conference on CSE, Fort Worth TX (Invited, March 2025)

• I am a recipient of the 2025 SIAM Postdoctoral Support Program (January 2025)

• Presented at the Joint Mathematics Meetings, Seattle WA (Invited, January 2025)

• Participated in the Blackwell-Tapia Conference, ICERM - Brown University (November 2024)

• Presented at Baby Inverse Problems (Zoom) Seminar (Invited, October 2024)

• Presented at the SIAM Central States Section Annual Meeting , Kansas City MO (Invited, October 2024)

• Presented in the M.E. Taylor Analysis and PDE Seminar, UNC-Chapel Hill (September 2024)

Research

My current research interests lie on inverse problems for Partial Differential Equations (PDEs). More precisely, I have been studying shape reconstruction problems arising from Electrical Impedance Tomography, Diffuse Optical Tomography, and inverse scattering. These projects focus on developing computationally inexpensive, yet rigorous algorithms. These problems require little a priori knowledge and arise in engineering and medical applications of non-destructive and non-invasive testing, respectively, as well as parameter identification. These non-destructive and non-invasive methods allow one to reconstruct defective regions by connecting them to known or partially constructed Cauchy data.

Research Interests: Qualitative Methods, Electrical Impedance Tomography, Diffuse Optical Tomography, Inverse Scattering, Asymptotic Analysis, Numerical Analysis, and Signal Direction of Arrival Estimation.

Publications

Submitted

1. G. Granados, J.L. Marzuola, and C. Rodriguez, "Recovering elastic subdomains with strain–gradient elastic interfaces from force measurements: the antiplane shear setting". Submitted (arXiv:2509.15171) 

2. G. Granados, I. Harris, and A. Kleefeld, "Direct and inverse scattering for an isotropic medium with a second-order boundary condition". Submitted (arXiv:2506.11818)

Refereed Publications

1. G. Granados, I. Harris, and H. Lee, "Reconstruction of extended regions in EIT with a generalized Robin transmission condition". Communications on Analysis & Computation, DOI: 10.3934/cac.2023017 (2023) (arXiv:2310.08223)

2. G. Granados and I. Harris, ''Reciprocity gap functional methods for potentials/sources with small volume support for two elliptic equations''. Applicable Analysis, DOI: 10.1080/00036811.2023.2279951 (2023) (arXiv:2302.05212)

3. G. Granados and I. Harris, "Reconstruction of small and extended regions in EIT with a Robin transmission condition". Inverse Problems, 38 105009 (2022) (arXiv:2203.09551)

Other Publications

1. G. Granados, Nicholas O'Donoughue, and Jonathan Roberts, "Retrodirection, MUSIC, and ESPRIT: Comparison of the Impact of Retrodirection on Array Processing Algorithms". RAND, RR-A1289-3, not available to the general public (2024)

2. G. Granados, “Asymptotic and Factorization Analysis for Inverse Shape Problems in Tomography and Scattering Theory.” Purdue University, Ph.D. Thesis (2024)