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This page highlights a selection of academic research and independent projects I'm currently working on and thinking about. If you want to learn more about past projects, particularly in areas like quantum computing and game theory, go here. If you want current updates on these projects and/or want to read some miscellaneous math content, go here.
Data Science Projects:
I'm relatively new to this field, but I am excited to pursue some interesting ideas.
Current projects of interest are:
A system by which you can put in your address and corresponding particulars, and get a detailed breakdown of both where your tax money goes and an approximate estimate and breakdown of the effective tax money you are receiving. ( on pause for time being but still relevant)
My group at UCSD (led by Professor David Meyer) was working on a project to determine whether we can measure the quantifiable effects of different levels of happiness using a large, privately shared data set. (finished)
I will speak more about this in the game theory section, but in brief, I am interested in using my research on balance in games and finding a system to test its validity and/or predictive potential.
Quantum Computing Projects:
This was the bulk of my academic work and a field that I am still very interested in pursuing both recreationally and careerwise.
Current projects of interest are:
SudoQ is a direct Quantum variant of Sudoku that has been introduced here, and studied here and here. As a lover of puzzles, especially Sudoku variants, I think there are still a lot of interesting, truly quantum, and maybe topological, SudoQ variants to be discovered. Specifically, I am developing several different quantum SudoQ variants that mimic standard Sudoku variants. such as killer sudoku, German Whispers, and kropki sudoku
Getting into the current practical research on Quantum implementation has been a goal ever since finishing the PhD. Most of my work, which is given below, is theoretical and hopefully relevant in creating a foundation for future Quantum devices; however, I want to understand the current-day issues and approximations that people are working on. I am currently doing a read-through of the literature to better understand how to best use NISQ devices on current projects. This research involves better understanding and creating implementations of:
A. Error Correction protocols on both trapped ion and superconducting devices
B. Error Mitigation and Error Suppression in the same context
C. Optimizing these for specific Quantum simulations e.g. DFT/ Quantum Chemistry
Game Theory Projects:
This was a small but significant part of my academic work. I find this subject as a whole very fun to think about, and everything feels like a kernel of a giant data-based undertaking.
Current projects of interest are:
Applying my work in unfair games and the associated food chain model to real food chains and seeing if there is predictive potential as an underlying theory of ecological interactions.
Applying the same work to different global and local markets and seeing if there is a way to make predictions. Maybe we could use some layered form of comparative advantage to define the game? We could see if this provides an answer to why there necessarily seem to be small and large companies that do various things.
Topology and Geometry Projects:
I think this field is so fun to think about, and there are little cute ideas that I want to explore in more depth.
Current projects of interest are:
Devise a metric of some sort (poset?) on geometries of the sphere such that all platonic solids are very high on said metric. Then use this metric to find the best almost platonic "n-sided" topological sphere. Motivation: In Dungeons and Dragons, you roll dice of several different sizes to determine the result of an action. The platonic solids are beautiful, and the others are truly disgusting. We should fix this.
Seifert surfaces are neat, and I think I should read about them and their connection with Khovanov homology more. If someone hasn't yet figured out a connection (which they probably have) maybe we can.
Circle packing is fun, do I have any interesting ideas? in the easy direction of course... in the hard direction not at all.
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