# Math

I was part of several research projects when I studied math. I was/am primarily interested in topology and algebraic invariants, but also did research on combinatorics and number theory.

## Research Projects

- In 2021, I studied knotted surfaces in dimension four with the Polymath Jr. REU. I wrote code to generate examples of knotted surfaces and understand their invariants.
- In 2020, I studied recurrence sequence and sum/difference sets at Williams College’s SMALL REU. I looked at generalizations of the Fibonacci sequence to figure out whether they could express every natural number as a sum of sequence terms (this property is called completeness).

## Papers

- Completeness of Positive Linear Recurrence Sequences
*Springer Proceedings in Mathematics & Statistics, vol 395, 2022.* - An Introduction to Completeness of Positive Linear Recurrence Sequences
*Fibonacci Quaterly, vol 58, no 5, 2020.* - Extending Zeckendorf’s Theorem to a Non-Constant Recurrence and the Zeckendorf Game on this Non-Constant Recurrence Relation
*Fibonacci Quaterly, vol 58, no 5, 2020.*

## Notes

## Talks

Click on a talk for slides, and replace `.pdf`

with `.tex`

in the link to download the LaTeX source.

- Knotted Surfaces in Dimension Four
*Polymath Jr REU Final Presentation*, Aug. 15, 2021 - Math in Base-Fibonacci: Recurrences and Complete Sequences
*Astronaut Technical Conference*, Aug. 14, 2021 - I gave a series of talks on algebraic topology at PROMYS 2021. Lecture notes are available.
- I gave a seminar on knot theory at PROMYS 2021. Lecture notes are available
- Completeness of Positive Linear Recurrence Sequences
*Combinatorial and Addtive Number Theory*, May 26, 2021 - More Sums Than Differences Sets in Finite Non-Abelian Groups
*Young Mathematicians Conference*, Aug. 14-16, 2020

Recording - Constructions of Generalized MSTD Sets in Higher Dimensions
*Young Mathematicians Conference*, Aug. 14-16, 2020

Recording - An Analytic Approach to Complete Generalized Fibonacci Sequences
*Young Mathematicians Conference*, Aug. 14-16, 2020

Recording - Completeness of Positive Linear Recurrence Sequences
*Northeast REU Conference*, Jul. 30, 2020*19th International Fibonacci Conference*, Jul. 22, 2020

Recording - How do Algebraic Curves Intersect
*UM Directed Reading Program*, Dec. 3, 2019 - Analysis on Fractals
*Seminar Class on Fractal Topology*, Dec. 7, 2018