I graded the homework for four classes throughout my junior and senior year of undergrad. I wrote comments to students on how they could improve their math skills and knowledge. These classes are Linear Algebra, Applied Complex Variables, and Number Theory.

Student Grader for four semesters:Complex Analysis in Fall 2021Linear Algebra in Spring 2022Number Theory in Fall 2022Complex Analysis in Spring 2023

Learning/Research experience with the Machine Learning and Evolutionary Laboratory at UofSC. I had the opportunity to explore the application of geometric deep learning to materials discovery. By training a graph neural network on known molecular formulae, we aimed to predict new materials similar to those inputted. During my time here, I started off by learning how to train GNNs using PyTorch Geometric. Then, I read academic papers on the current state of deep learning driven materials discovery. Finally, I helped modify and train a GNN to suggest molecular formulae based on a masked input.

Biomathematical modeling research with Dr. Vasquez. My researched focused on simulating the stress granule formation of mRNA. Programming languages used include Python and MATLAB.

From Nov. 15th - Nov. 28th, I attended the Masamu Advanced Study Institute and SAMSA conference in Maputo, Mozambique and found other mathematicians to collaborate on a pure maths problem of our choice. I explored a problem I previously worked on during my REU at Auburn, finding a closed solution to the Frobenius coin problem in three variables. In the end, I theorized a geometric algorithm to partition the FC problem into 4 main cases, each having an infinite amount of subcases, and visualized the algorithm in Python. I found an exact equation for the second layer of each case, and the rest of was passed on to future REU students to complete.

During this REU (Research Experience for Undergraduates), I developed software to simulate the thermal fluctuations of small linear strands of DNA using C++. This involved calculating eigenvectors and eigenvalues to determine the paths of least resistance for base pairs and the probability that any base pair would randomly move. My output files were pdb files, which could be visualized in PyMOL.I also analyzed large amounts of empirical energy deformation data using Python. Along with using this data to calculate the step parameters, I was able to generate heat maps showing the flexibility of step parameters as well as the interdependence between any two step parameters.

During this REU, I worked on two research projects, both related to the Frobenius Coin problem. During the first half of my summer, I theorized and proved a solution for a version of the FC problem in the Gaussian integers, publishing the work in Geombinatorics in April of 2022. During the latter half, I worked with a team on finding a closed-form solution to the classical FC problem in three variables. Along with another REU student, we worked off past students' work, correcting their theorem and providing strong computational evidence for our version. I presented our work virtually at SAMSA (Southern Africa Mathematical Sciences Association) in Nov. 2021, and later furthered our work next year when I joined Masamu as a research collaborator.