I am interested in height functions on the space of algebraic numbers and equidistribution. Here is my research statement.
Adelic Heights Associated to Sequences of Rational Maps. In preparation.
In this work, I prove that under natural assumptions, there exists an adelic measure for a sequence of rational maps defined over a number field. Slides from a recent talk.
Areal Weil Heights. In preparation.
I construct and study a family of adelic heights inspired by the areal Mahler measure. arXiv preprint coming soon!
Bounds on the Mahler Measure of a Composition (joint with Jeff Vaaler). In preparation.
Addressing a question of Granville, we find bounds for local and global Mahler measures of polynomial compositions.
I participated in the CSUSB REU during the summer of 2022. Here is the paper that I wrote for it: