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

Incidences among flows

joint with Kaiyi Huang and Betsy Stovall

arXiv

Incidence bounds related to circular Furstenberg sets

joint with John Green, Terence L.J. Harris, Yumeng Ou, and Kevin Ren

arXiv

Incidence Estimates for Tubes in Complex Space

joint with Lingxian (Rose) Zhang

arXiv

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

journal | arXiv

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.