Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

The first part of the talk is to study a modified version of mean curvature flow, the ``conformalized mean curvature flow" (cMCF), originally introduced by Kazhdan, Solomon, and Ben-Chen. The cMCF can be used to compute discrete conformal maps from any meshes of closed genus-zero surfaces onto a sphere but it runs into numerical issues when it is applied on meshes with protrusions. We improve the cMCF with an initialization step which maps the initial mesh onto a sphere. This initialization step is shown to improve the performance of cMCF such that it can be applied on meshes with long protrusions.

The second part of this thesis focuses on a project in computer tomography. Our work is to reconstruct the 3D X-ray emission distribution of the nuclear fusion hotspot from a very limited number of 2D X-ray projection images. Such 3D X-ray reconstruction can help us characterize and compare the thermophysical states of the fusion plasma such as its temperature. We apply and test the algebraic reconstruction technique (ART) to the reconstruction of the 3D X-ray emission distribution of the nuclear fusion hotspot. Furthermore, we come up with a method to make inference on the 3D hotspot electron temperature distribution by using our 3D X-ray reconstructions.