Divyansh Agrawal receives “Honourable Mention” for his PhD thesis

Divyansh Agrawal has received honorable mention for his thesis titled

Uniqueness and range characterization in inverse problems.

from the TIFR Alumni Association (TAA) as part of the TAA-Harish Chandra Memorial Awards in Mathematics for 2026. The citation from the award committee states

For contributions to the study of unique continuation and range characterization results of several integral transforms arising in inverse problems

About the thesis work

The inversion of integral geometric transforms plays a significant role in both theoretical and applied inverse problems. Important examples include the Radon transform, the X-ray transform of functions, vector fields, and symmetric tensor fields, the spherical mean transform, and the light ray transform. A central theme of Divyansh’s research is unique continuation and its failure for such transforms.

One of his earliest works established unique continuation results for the ray transform of symmetric tensor fields. In studying the inversion of the spherical mean transform in odd dimensions, he obtained range characterizations and demonstrated the failure of unique continuation. In subsequent work, he investigated the kernel of the associated backprojection operator and disproved a conjecture of Boris Rubin in odd dimensions. He also established unique continuation results for d-plane transforms, including the Radon transform. Finally, his research on the light ray transform of functions in pseudo-Euclidean spaces yielded stability estimates for this transform. Taken together, these results significantly clarify both the reach and the limits of unique continuation in integral geometry.