Mathematician/Academic Consultant
I Served as a Mathematician and Consultant for multiple start-ups, where I applied my academic training to study their field and develop a theoretical basis for their technology. In doing so, I developed proofs and mathematical models to be used in white papers and utilized mathematical rigor to rewrite and reorganize grant applications so that external experts could easily understand the technical reasoning and the commercial value of their innovations.
- Mathematically modeled and made rigorous the approach used by a signal processing startup, named Terawave, by researching and becoming well-acquainted with the mathematical methods used in signals and systems.
- Assisted engineers in utilizing new methods by clearly explaining the current state of the art and how we could precisely apply it to the situations at hand.
- Researched the inner workings of their blockchain method for a startup named Notoros, and utilized these results to both double-check the feasibility of their methods, as well as to communicate them carefully so that industry experts could clearly and easily understand their research.
- Dived heavily into the theory behind Waste-to-Energy conversion for a startup named enVerde to assist in their applications for research grants.
Graduate Researcher
In my academic research, I focused on topological quantum information specifically exploring the encodings of various topological invariants as code spaces within quantum error-correcting codes. Additionally, I contributed to projects in game theory, where I developed a toy model to analyze unfairness in undominated games. These endeavors demonstrated my ability to apply complex theoretical concepts to practical problem-solving in quantum computing and game theory.
- Studied and became well-acquainted with quantum algorithms, quantum error correction, and topological quantum information.
- Developed an encoding of characteristic classes, specifically obstruction classes of fiber bundles, for quantum error correction, using a novel encoding of homological and cohomological codes that extend Kitaev's toric codes.
- Studied and worked on developing a framework for classifying certain higher dimensional topological codes that act similarly to Levin-Wen and Walker-Wang structures.
- Defined a new and unconventional model for unfairness within certain undominated and strictly undominated games, and used it to find the least fair forms of 2-player Rock-Paper-Scissors and prove the existence of an unfair form of Rock-Paper-Scissors for less than 100 players.
- Modeled populations in ecological hierarchies leveraging the novel form of unfairness to describe stable yet unbalanced population dynamics.
- Advised students of Professor Meyer on strategies to clean, display, and utilize data more effectively.
Lecturer and Teaching Assistant
I served as a Teaching Assistant, and Lecturer for a wide range of mathematics courses at the University of California San Diego (UCSD). Additionally, I held the role of lead Matlab coordinator for the UCSD Mathematics Department, overseeing the integration and support of Matlab resources across the department's curriculum.
- Lectured multivariable calculus to a class of 200 students.
- Coordinated the MATLAB curriculum for linear algebra and differential equations, serving over 1,000 students per semester, including managing teams of 15-20 graders and tutors to ensure timely and effective support and feedback.
- Served as a Teaching Assistant for nearly every undergraduate math class offered at UCSD, and the entire graduate topology sequence.
Software Engineering/Physics Intern
During my gap year, I worked at an infrared technologies start-up, serving as an apprentice software engineer, and developing software interfaces for infrared detectors. I also led the team in drafting grant applications, leveraging my technical writing skills to support project development.
- Developed software in C# to process data from an infrared detector, converting it into black-and-white values, cleaning the data, and generating the corresponding visual output.
- Constructed multiple optional tools to enhance visual output, including edge-detection, screen recording, and customizable toolbars for manual data cleaning adjustments.
- Led a successful Phase I SBIR NSF grant application, overcoming a competitive acceptance rate of under 20%, by effectively translating complex physics concepts into clear, accessible language for the NSF review team.
Undergraduate Researcher
I contributed to multiple research projects in Alexey Kolmogorov's computational physics group, furthering my expertise in machine learning methods, computational mathematics, and collaborative research environments.
- Studied and constructed Gaussian processes in C for possible applications in using machine learning to predict potential superconductors.
- Used Professor Kolmogorov's Maise/AI software to better understand graphene energy transitions.
- Produced computational models in C for predicting the behavior of the three-torus under unstable diffeomorphisms.
UCSD
This is my Dissertation, which is available on ProQuest. It contains current copies of the three papers below.
Under Review
This work outlines new methods for topological encodings in quantum error correcting codes.
Under Review
This work discusses a novel form of unfairness in games.
In Preparation
This work assists in classifying a certain form of topological codes.
Experimental Mathematics
A project using computational evidence and numerical methods to understand the behavior of an unstable dynamical system acting on the three-dimensional torus.
Journal of Physical Chemistry
A study in the full reduction process for Iron-Oxide nanowires.