I am an Associate Professor in the Math Department. Before coming to UCSB, I was a Postdoctoral Research Associate at the University of Cambridge, 2015-2017, working with Prof. Gabriel Paternain. I received my PhD in Mathematics from the University of Washington in 2015, and my PhD advisor is Prof. Gunther Uhlmann.

Fall 2024: Math 119A ODE's; Math 260F Seminar in Math

PhD students: Pranav Arrepu (2023-present)

Postdoc: Kelvin Lam (2024-present); Ashwin Tarikere (2020-2023)

My research focuses on the mathematical analysis of inverse problems and their connections with concrete applications, often motivated by problems arising in medical imaging, geophysics, classical and quantum mechanics, and astronomy, among other areas. It is at the interface of several disciplines including partial differential equations, microlocal analysis, differential geometry, and mathematical physics.

I am available to supervise both undergraduate senior theses and graduate students. You are welcome to contact me if you are interested in my research area. Research assistantships for graduate students are available.

My research is partly supported by the NSF grant DMS-2109116 and DMS-2408369.

*The weighted X-ray transform and applications*, to appear in "Microlocal Analysis and Inverse Problems in Tomography and Geometry", Proceedings of Linz Workshops on Inverse Problems.*Stability and statistical inversion of travel time tomography*, (with A. Tarikere), to appear in Inverse Problems.*On the identifiablility of nonlocal interaction kernels in first-order systems of interacting particles on Riemannian manifolds*, (with S. Tang, M. Tuerkoen), to appear in SIAM Journal on Applied Mathematics.*Recovery of coefficients in semilinear transport equations*, (with R.-Y. Lai, G. Uhlmann), to appear in Archive for Rational Mechanics and Analysis.*Single pixel X-ray transform and related inverse problems*, (with R.-Y. Lai, G. Uhlmann, J. Zhai), SIAM Journal on Imaging Sciences, 15 (2022), 1894-1909.*Inverse source problems in transport equations with external forces*, (with R.-Y. Lai), Journal of Differential Equations, 302 (2021), 728-752.*Unique determination for an inverse problem from the vortex dynamics*, (with R.-Y. Lai), Inverse Problems, 37 (2021) 025001.*Travel time tomography in stationary spacetimes*, (with G. Uhlmann, Y. Yang), Journal of Geometric Analysis, 31 (2021), 9573-9596.*Travel time tomography*, (with P. Stefanov, G. Uhlmann, A. Vasy), Acta Mathematica Sinica, 35 (2019), 1085–1114.*Lens rigidity for a particle in a Yang-Mills field*, (with G. Paternain, G. Uhlmann), Communications in Mathematical Physics, 366 (2019), 681-707.*Reconstruction of a compact Riemannian manifold from the scattering data of internal sources*, (with M. Lassas, T. Saksala), Inverse Problems and Imaging, 12 (2018), 993–1031.*Generic injectivity and stability of inverse problems for connections*, Communications in Partial Differential Equations, 42 (2017), 780-801.*The local magnetic ray transform of tensor fields*, SIAM Journal on Mathematical Analysis, 50 (2018), 1753-1778.*The geodesic X-ray transform with matrix weights*, (with G. Paternain, M. Salo, G. Uhlmann), American Journal of Mathematics, 141 (2019), 1707–1750.*Lens rigidity with partial data in the presence of a magnetic field*, Inverse Problems and Imaging, 12 (2018), 1365-1387.*Journey to the Center of the Earth*, (with G. Uhlmann), submitted to the Proceeding of the XVIII International Congress on Mathematical Physics.-
*Invariant distributions and the geodesic ray transform*, (with G. Paternain), Analysis & PDE, 9 (2016), 1903-1930. -
*Injectivity and stability for a generic class of generalized Radon transforms*, (with A. Homan), Journal of Geometric Analysis, 27 (2017), 1515-1529. -
*Invariant distributions and tensor tomography for Gaussian thermostats*, (with Y. Assylbekov), Communications in Analysis and Geometry, 25 (2017), 895-926. -
*An inverse kinematic problem with internal sources*, (with L. Pestov, G. Uhlmann), Inverse Problems, 31 (2015) 055006. -
*Boundary and scattering rigidity problems in the presence of a magnetic field and a potential*, (with Y. Assylbekov), Inverse Problems and Imaging, 9 (2015) 935-950. -
*Local X-ray transform for a general family of curves*, appendix to The inverse problem for the local geodesic ray transform by G. Uhlmann and A. Vasy, Inventiones Mathematicae, 205 (2016) 83-120. ( Expanded version:*The inverse problem for the local ray transform*)

- International Zoom Inverse Problems Seminar
- International Conference and School on Inverse Problems, SCMS, Shanghai, China, June 24-July 3, 2024

- UCSB Math Seminars and Colloquia
- Inverse Problems Conferences: Source 1; Source 2

- Math 8: Transition to Higher Mathematics
- Math 117: Methods of Analysis
- Math 118: Introduction to Real Analysis
- Math 119: ODE's
- Math 201: Real Analysis (graduate)
- Math 206D: PDE's Finite Element Method
- Math 243: ODE's (graduate)
- Math 246: PDE's (graduate)
- Math 260: Seminar in Math: Fall 2018, Winter 2020; Spring 2021; Spring 2023