Some Projects
On this page, you can find some of my longer projects. I have separated them into categories for convenience. The exception is things I have done before college which are grouped to together in the last category. Feel free to contact me about any of the projects below :)
Computer Science
A domain-specific programming language I’m building along two classmates. The basic premise is that you write down a tree diagram in an extremely intuitive syntax where the amount of indentation indicates the current depth level in the tree and then our language visualizes the tree graph for you. We hope that it finds applications in family trees, taxonomy, graph theory, consulting, and more. So far we have a functioning ANTLR grammar as well as a working lexer and parser.
Quantitative Finance
In this paper, we propose S&P N indices that track market cap weighted portfolios of the largest N publicly traded companies on US exchanges. First, we discuss the specifics about the construction of each portfolio. Then we calculate a historical Sharpe ratio for each index over a month for 6 months. Last, we produce a forward looking 1 month Sharpe ratio for each S&P N index and compare the results to the historical ones. We perform a Spearman correlation coefficient testing to compare the two methods of calculation.
Abstract: In this paper, we propose an alternative way to calibrate one-factor interest rate models. Instead of using the interest rate yield curve, we suggest that they are anchored to the interest rate futures curve. We implement the Ho-Lee model due to its simplicity and tractability. We fitted this model to the 3 month SOFR futures curve and used it to predict zero-coupon bond prices. Finally, we suggest future steps to expand on a more sophisticated volatility function and using r ∗ (neutral interest rate) as the mean reverting term in the drift function.
Theology
- On Universalism (coming soon)
An incoming article I’m currently writing for the 2024 Fall issue of the Dartmouth Apologia. It gives a defense of Trinitarian Universalism arguing that universal single predestination should be the default position based on the intuitive case and that no argument is sufficiently strong to rise to the burden of proof required to overthrow it.
Older
Abstract: A “greedy” sequence is a number sequence of non-negative integer in which the first member is 0 every next member is defined as the smallest integer larger than the last term such that a certain equation is avoided for two or more terms. We start by analyzing the Stanley Sequence (avoiding arithmetic progression) beginning with 0, 1, and construct a non-recursive formula for calculating its terms. We then define some notation and move on to analyzing different greedy sequences. We use different numerical systems to do so and try to conjecture what can be achieved by this approach.
I won a few national competitions with this project and presented it at Expo Sciences Luxembourg. I also won a silver medal at the 2021 ICYS.
Abstract: Since Russell’s paradox was pointed to Frege, the logicism movement with the exception of the neo-logicists has been largely abandoned. In this paper, Frege’s semantic system is revisited and his arguments are refuted to show that numbers are not objects but concepts, and more specifically– properties. It is shown there are needed to distinguish between entities and a logical definition of such distinctions is given. Singular terms and predicates are also revised to show that the new system can benefit from Hume’s principle and can enjoy the results from Frege’s theorem.
I worked on this with Dr Owen Griffiths (Churchill College, Cambridge) on a scholarship from the Cambridge Center for International Research back in my last high school Summer.
Abstract: We give a language and a set Σ of sentences of that language such that any structure A that is a model of Σ is a vector space over Q. We then give sets Γn for each n such that the vector space given by A is of dimension n or more exactly when A satisfies Γn with some variable assignment. Then we show that Cn(Σ) is incomplete and discuss what extensions make it complete. Throughout the paper we consider how our conclusions would differ if the vector spaces we were considering were over a finite field F instead of Q. Finally, we discuss the implications of these results for determining the dimension of a vector space given by such a structure A.
A short commentary on Frege’s arguments from the Grundlagen that supposedly refute the notion that natural numbers are properties. I critique these arguments as part of a preparation for the Cambridge project described above.