I am a fifth year mathematics Ph.D. candidate at the University of California, San Diego. Rayan Saab is my adviser. I received my bachelor’s degree in mathematics at the University of Georgia in 2015. For anyone who is interested, here is a copy of my CV and my resume.
My research interests lay primarily in digital signal processing, and quantization. A central goal of my research is to study how to approximately reconstruct structured signals embedded in a high dimensional space from very few quantized measurements. Importantly, I am interested in quantization schemes where the error incurred from quantization decays polynomially or exponentially fast with respect to the number of measurements.
Additionally, I’m interested in random matrix ensembles as seen in the compressed sensing literature as well as non-linear random measurement operators which appear in the phase retrieval and blind deconvolution settings. I am also interested in the asymptotic case, where one uses tools from free probability to study the empirical spectral distributions of random linear operators. The latter case appears in modeling large scale communication networks with random network topologies as well as in MIMO systems.
In the spring of 2017 the signal processing group at UCSD went through recent advancements in deep learning from the perspective of applied harmonic analysis. I’ve written a blog post about one of the papers we read if you’re looking for a nice introduction.
As an undergraduate, I worked with Jason Cantarella on computational knot theory.
With the help of Patty Wagner and a few of my then colleagues I helped record and uploaded lectures of the MATH 3500/3510 course at UGA. You may find those lectures at the following YouTube page.