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 2021: Math 118A Introduction to Real Analysis

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 and graduate students. You are welcome to contact me if you are interested in taking reading courses and doing research with me.

*Inverse source problems in transport equations with external forces*, (with R.-Y. Lai), submitted.*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), to appear in Journal of Geometric Analysis.*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
- Special Semester on Tomography Across the Scales, RICAM, Linz, Austria, Fall, 2021

- Math 8: Transition to Higher Mathematics: Spring 2018, Winter 2020;
- Math 117: Methods of Analysis: Winter 2018, Spring 2018;
- Math 119: ODE's: Winter 2021;
- Math 201: Real Analysis (graduate): Spring 2021;
- Math 206D: PDE's Finite Element Method: Fall 2018;
- Math 243: ODE's (graduate): Spring 2020;
- Math 246: PDE's (graduate): Spring 2019;
- Math 260: Seminar in Math: Fall 2018, Winter 2020; Spring 2021