Yilin Ma

School of Mathematics and Statistics

Carslaw Building (F07) University of Sydney NSW 2006

K.Ma@maths.usyd.edu.au

The Inverse Conductivity Problem

Welcome to my academic website! I am a research master’s student at the University of Sydney. I work on the theory of inverse problems with Professor Leo Tzou. I obtained my undergraduate degree also from the University of Sydney in pure mathematics. Prior to my study of inverse problems, I worked with Professor Ben Goldys on stochastic partial differential equations (SPDEs) and wrote a thesis on the application of Fourier analysis to singular SPDEs. Here is my CV.

I was suggested to upload a picture of myself but was too shy to do so.

What are Inverse Problems?

Most of us have some ideas of how a CAT scan looks like: you wait patiently until your body has been through a large circular machine, and with your skin intact, everything inside you magically becomes visible from a computer screen. In other words, you have just seen the unseen! The mathematical theory behind such a procedure is an inverse problem.

The above example is classical and is based on the so called Radon transform. But it is really the 1980s groundbreaking result of Sylvester-Uhlmann on the Calderón problem that sparked new innovations in this direction. Physically, the Calderón problem asks the following question of oil prospection: can one determine the electrical conductivity of an object by making voltage to current measurements? For a quick mathematical description of the problem, see this article.

Most inverse problems arise from ideas in non-invasive imaging and are thus traditionally considered on bounded flat domains with sufficiently regular boundaries. It is my interest to see how these problems behave if the underlying geometries are replaced by much more interesting ones.

Preprints :

  1. A note on the partial data inverse problems for a nonlinear magnetic Schrödinger operator on Riemann surface, arXiv:2010.14180. (Download from arXiv)
  2. The Calderón problem in the $L^p$ framework on Riemann surface, arXiv:2007.06523. (Download from arXiv)

Publication：

  1. Semilinear Calderón problem on Stein manifold with Kähler metric (with L. Tzou), Bulletin of the Australian Mathematical Society, 103(1), 2021. (Download from publisher)

Talks:

  1. The Calderón problem with unbounded potentials in two dimensions. (Slides)
  2. Semilinear Calderón problems on complex manifolds. (Slides)