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

• Constructing the Derived Category

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