## Research

I am generally interested in algebraic invariants, and especially in applications of homological algebra to algebraic topology. My past research has been in combinatorial number theory, studying complete recurrence sequences and more sums than differences sets, and in low dimensional topology, studying knotted surfaces in dimension four.

### Research Experience

- I studied knotted surfaces in dimension four as part of the Polymath Jr. REU. I wrote code to generate examples of knotted surfaces and understand their invariants.
- I did research in combinatorial number theory at the SMALL REU at Williams College in 2020, leading to several publications in the Fibonacci Quarterly and presentations at research conferences including the International Conference on Fibonacci Numbers and Their Applications and the Young Mathematicians Conference. My work was on generalizations of the Fibonacci numbers as well as more sums than differences sets.
- I participated in the Directed Reading Program at U of M during the fall semester 2019, where I studied algebraic curves with Aleksander Horawa.

### Mentoring

- I mentored students at PROMYS in 2021 on a research project involving game theory, group theory, and geometry.
- I was a teaching assistant for the Eureka research program for high schoolers in 2020 on a project about nonlinear recurrence sequences. Their work was presented at the International Conference on Fibonacci Numbers and Their Applications and lead to a publication in the Fibonacci Quarterly.

### Papers

*Completeness of Positive Linear Recurrence Sequences*(with E. Boldyriew, P. Lam, J. Lentfer, S. J. Miller, and F. Trejos-Suarez), preprint.*An Introduction to Completeness of Positive Linear Recurrence Sequences*(with E. Boldyriew, P. Lam, J. Lentfer, S. J. Miller, and F. Trejos-Suarez),*Fibonacci Quarterly*58 (2020), no. 5. https://www.fq.math.ca/Papers1/58-5/boldyriew2.pdf.*Extending Zeckendorf's Theorem to a Non-Constant Recurrence and the Zeckendorf Game on this Non-Constant Recurrence Relation*(with E. Boldyriew, A. Cusena, L. Dai, A. Dunkelberg, P. Ding, K. Huffman, D. Ke, D. Kleber, J. Lentfer, T. Luo, S. J. Miller, C. Mizgerd, V. Tiwari, J. Ye, Y. Zhang, X. Zheng, and W. Zhu),*Fibonacci Quarterly*58 (2020), no. 5. https://www.fq.math.ca/Papers1/58-5/boldyriew1.pdf.- Contributed to
*Constructions of Generalized MSTD Sets in Higher Dimensions*(E. Kim and S. J. Miller),*Journal of Number Theory*, vol 235, pp. 358-381.