Research
My research is in Fourier analysis. I am particularly interested in connections between Fourier analysis and incidence geometry. I am also interested in restriction theory, decoupling, and applications to analytic number theory.
As an undergraduate, I was part of the Geometry Group at the SMALL REU, where we studied isoperimetric problems.
Selected Publications and Preprints
Incidence Estimates for Slabs
in preparation
Incidence Estimates for Tubes in Complex Space
joint with Lingxian (Rose) Zhang
submitted
Isoperimetric Regions in R^n with Density r^p
joint with Wyatt Boyer, Bryan Brown, Gregory R. Chambers, and Alyssa Loving
published in Analysis and Geometry in Metric Spaces
PhD Thesis and Defense
In my PhD thesis, I studied incidence problems for slabs which consist of the delta-neighborhoods of well-spaced hyperplanes. Under one spacing condition, I proved an estimate for the number of lattice boxes that can be r-rich for such a collection of slabs.
Here is a link to the text of my thesis.
Here is a link to the slides I made for my thesis defense.