Updated: Mar 11, 2021
I work in some of the more abstract parts of mathematics, but I also seek out situations where the theoretical ideas can be put to good use in the sciences.
As a graduate student, I wrote a paper with Prof Kindt at Emory where we used these mathematical ideas in the modeling of compound and particle formation. The mathematics formed the basis of a robust model which made precise predictions which could later be tested.
Imagine you have a sphere in R^3 with radius equal to the square root of n. How many points with integer coordinates are there on this sphere? Gauss gave a formula in Disquisitiones Arithmeticae relat
Say you want to know how many ways you can write n as a sum of positive integers, up to reordering the summands. The number of ways is the nth partition number p(n). 100 years ago, Ramanujan discove
The study of L-functions such as the Riemann zeta function is one of the most classical fields of analytic number theory. The distribution of zeros of L-functions encode arithmetic information such as