Research

Presentations

• October 6, 2021, Rowan University Department of Mathematics Colloquium, "p-adic Valuations of Quadratic Sequences"

• September 22, 2021, Penn State Student Number Theory Seminar, "p-adic Valuations of Quadratic Sequences"

• August 7, 2021, MathFest MAA Student Paper Sessions, "p-adic Valuation Trees of Quadratic Polynomials"

• July 23, 2021, Ursinus College Summer Fellows Symposium, "p-adic Valuation Trees of Quadratic Polynomials"

Publications

• Will Boultinghouse, Emily Hammett, Stephen Hu, Olena Kozhushkina, Rachel Snyder, and Justin Trulen. p-adic Valuations of Quadratic Sequences. Submitted for publication. https://arxiv.org/abs/2309.16637.

Research Interests

During my undergraduate studies, my primary interest was number theory, specifically analytic number theory. I have worked on two main projects in analytic number theory, one regarding generalizations of the Bernoulli and Euler polynomials and numbers, and one regarding p-adic sequences.

I am now interested in numerical analysis. I am working on a project that involves applying numerical methods to partial differential equations.

Research History

• Summer 2023 - Present: I am doing research in numerical analysis under the mentorship of Dr. Ludmil Zikatanov and Dr. Kenneth Czuprynski. This project involves applying numerical methods to partial differential equations.

• Summer 2021: As part of a Research Experience for Undergraduates (REU), I did research with two other students under the mentorship of Dr. Olena Kozhushkina at Ursinus College in Collegeville, PA. We researched p-adic valuations of quadratic sequences and examined the connections between the polynomials and the corresponding tree representations. This work was within the field of analytic number theory. We collaborated with a student and his mentor Dr. Justin Trulen at Kentucky Wesleyan University.

• Fall 2019 - Spring 2021: I did research with one other student under the mentorship of Dr. Abdulkadir Hassen at Rowan University in Glassboro, NJ. We worked on generalizing the Bernoulli and Euler polynomials and numbers. This work was within the field of analytic number theory.

• Spring 2020: As part of a course under the Preparation for Industrial Careers in Mathematics (PIC Math) program, I did research with four other students under the mentorship of Dr. Thanh Nguyen at Rowan University in Glassboro, NJ. We researched brain stroke detection using microwave imaging. This work involved partial differential equations and numerical techniques for their solution.