Yuxuan Song

I am a PhD student working under the supervision by Prof Felix Schulze and Dr Maxwell Stolarski. I am primarily interested in differential geometry and non-linear PDEs, more specifically in the regularity theory and singularity theory for minimal surfaces and mean curvature flows. Often questions arising in these fields can be tackled using tools from elliptic PDEs, spectral analysis and geometric measure theory.

Prior to starting my PhD, I was an undergraduate student in the Department of Statistics at Warwick. I am/was known to dabble around topics in quasi-contact geometry and sub-Riemannian geometry, with my masters thesis supervised by Dr. Karen Habermann.

Here are some materials on sub-Riemannian geometryLink opens in a new window and the structure of Radon measures on LCH spaces.Link opens in a new window The former contains some metric-geometric aspects of the subject, which probably holds in greater generality. The latter is some content which is typically not covered in a first course in measure theory/functional analysis, but somehow assumed in many graduate-level courses in analysis. Highly motivated undergraduate students (enthusiastic enough to tackle topics outside the scope of their modules) and some graduate students might benefit from having a look at these. I certainly wish that I learnt these materials as early as possible (immediately after having learnt the Hahn-Banach theorem, say). Neither of these two documents has been carefully maintained so I would appreciate any comments/corrections.

I may be reached by email at yuxuan (dot) song (at) warwick (dot) ac (dot) uk.

_{*According to the department's policy I need to have a section on conferences/workshops I have attended or will be attending, so here it is.}