Broadly, my mathematical research interests are compressive sensing, high dimensional function approximation, numerical PDEs, and high performance computing.
I am especially interested in developing theoretically sound numerical methods related to these fields and enjoy developing high quality code to complement them.
More specifically, I am interested in applying techniques adjacent to compressive sensing to recovering functions which have sparse expansions in various polynomial bases. Some of my recent work along these lines has involved proving recovery guarantees for fast algorithms which compute sparse high dimensional Fourier transforms. Additionally, I have used these techniques to quickly solve simple high-dimensional PDE via a sparse Fourier spectral method.
In my undergraduate, I worked on implementation of finite element methods using serendipity basis functions.
|C.G., M. Iwen, L. Kämmerer, T. Volkmer||Sparse Fourier transforms on rank-1 lattices for the rapid and low-memory approximation of functions of many variables [arxiv] [pdf] [code] [BibTeX]||2022||Sampling Theory, Signal Processing, and Data Analysis|
|C.G., M. Iwen, L. Kämmerer, T. Volkmer||A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size [arxiv] [pdf] [code] [BibTeX]||2021||Advances in Computational Mathematics|
|A. Gillette, C.G., K. Plackowski||Numerical studies of serendipity and tensor product elements for eigenvalue problems [arxiv] [pdf] [code] [BibTeX]||2018||Involve (Undergraduate publication)|