In high-school, I’d frequently document my calculus and geometry ideas, pushing the boundaries of the course material with diverse techniques. Everyday I’d pursue these ideas with my class material to no avail. I live in a Black, low-income neighborhood with no peers my age in college, no physics labs, no professors, and scant STEM knowledge available for exchange. Available textbooks lacked depth in my areas of interest, thereby hindering my desires to answer questions about mathematics. With no mentorship, advice, and science literature available, I lacked the resources needed to craft my ideas into something viable. Undergraduate at Williams College opened opportunities for me to nourish my mathematics and physics knowledge. My research …show more content…
Following a summer science program offered by my college (Williams College) as an incoming freshman, I was offered to work as a research assistant with Professor Cesar Silva, a Hagey Family professor of the college. Professor Silva introduced me to LaTeX, the Collatz Conjecture, and elementary fractal structures. We worked on studying modified versions of the Collatz conjecture, or the ‘3k+1’ problem, through Java programming. While performing these experiments, I noted to Professor Silva that the Collatz Conjecture behavior resembles an object that enters a gravitational orbit because integers would “swing around” the center (ie. the number 1) while greatly decreasing in size. In the following semester, I worked with Professor Mihai Stoiciu on fractal algebra and geometry. Most of my projects involved creating fractal images using Wolfram Mathematica. There was so much joy while learning the mathematics behind beautiful fractal structures and creating them myself. My most research experience was with Professor Frederick Strauch in January, and this was my first physics-based research project. I studied elementary quantum processes with qubits, the Hilbert space, and Grover’s algorithm. We plan to apply quantum searching techniques to understand …show more content…
While learning geometry, real analysis and calculus, I’ve taken an interest in applying mathematical methods to describe particles that travel with wave-like behavior. Wave dynamics govern the images and sounds perceived everywhere, and they also describe the behavior of fundamental particles found in the universe. Specifically, my interests vests in understanding gravitons and interactions between sets of gravitons. Gravitons are theoretical, and as of today have not been discovered; however, it is possible that they are the byproduct of subatomic particle interactions. These processes produce quantities of graviton energy that is both stored inside the mass and released in to space, thereby causing mass-induced