Research Interests for Robert J. Ravier
In undergrad, I was one of many people involved in a (still ongoing) effort to move classical analysis into the world of fractals. I was involved in two projects. The primary one was related to sampling theory. In general, it turns out that natural analogues of the Shannon Sampling Theorem don't exist for general post-critically finite fractals. However, they do exist in certain cases, such as the Sierpinski gasket. I also spent a brief time analyzing nonlinear PDE via numerical variational methods in the fractal setting.
I'm currently still searching for which area to continue my pursuits. In general, I'm interested in problems related to analysis or PDE, particularly those of a geometric flavor.
- Areas of Interest:
- Geometry Processing
High dimensional data analysis
- Recent Publications
- R. Ravier, R. Strichartz, Sampling Theory with Average Values on the Sierpinski Gasket
(Submitted, May, 2013) [arXiv:1308.0079], [pdf] [abs] [author's comments]