Mathematics · Quantitative Research · Machine Learning
I combine mathematical research with programming and computational experimentation to develop and evaluate methods in machine learning, statistical modeling, and scientific computing. My projects include drug and vaccine safety signal prioritization, kernel methods, and mathematical visualization, alongside ongoing research on portfolio compression and deep hedging.
I use AI and large language models as conjecture engines to generate candidate formulas, explore algorithms, and develop possible proof strategies. I critically evaluate these ideas through counterexample searches and reproducible computational experiments, and establish mathematical results through rigorous proof. My strength is connecting theory with implementation: understanding how a method works, evaluating its performance, and identifying the assumptions and limitations that matter in practice.
I am studying how low-dimensional representations of financial portfolios affect hedging decisions. The project connects mathematical bounds on representation and learning errors with Bellman-based benchmarks and the development of neural-network trading strategies, accounting for transaction costs and trading constraints.
I developed and evaluated gradient-boosted models to prioritize drug–adverse-event reporting signals in the FDA Adverse Event Reporting System (FAERS). The study combines classical disproportionality measures with report-quality information and examines performance on future quarters, calibration, and the contribution of different feature groups.
Using the Vaccine Adverse Event Reporting System (VAERS), I built a workflow that ranks vaccine–symptom pairs by their likelihood of meeting a reporting-signal criterion in the following quarter. The project compares logistic regression and calibrated gradient boosting with classical statistical scores to prioritize pairs for expert review.
The target is a future statistical reporting signal used for triage, rather than a causal estimate of vaccine risk.
In joint work with Emeric Battaglia, I study stochastic gradient descent for complex-valued kernel regression. The project combines convergence and directional-bias analysis with numerical experiments in complex reproducing kernel Hilbert spaces, including the recovery of superoscillatory functions and Blaschke products.
As an undergraduate researcher working with Mihaela Vajiac, I studied and implemented classification methods, including perceptrons, radial basis function networks, and support vector machines, using Python and MATLAB. The project connects the mathematical foundations of these methods with numerical experiments and visualizations of decision boundaries.
Working with Peter Jipsen, I developed JavaScript visualizations of finite lattices using Babylon.js. The project renders algebraic structures as interactive 3D objects that can be explored in a web browser or with a virtual reality headset.
I analyzed New York City motor vehicle collision records, using data cleaning and visualization to examine recorded crash characteristics and changes around the COVID-19 pandemic. The project focuses on descriptive comparisons and patterns in the reported data.
I applied ARIMA and Holt–Winters models in R to financial time series. The project focused on fitting statistical models, examining trends, and producing and visualizing forecasts.
I built a Python and SQL web interface for exploring data about the 118 chemical elements. The project connects a relational database with an interface for querying and displaying element properties and their relationships.
I implemented binary search trees and red-black trees in C++, studying how tree balancing supports efficient search and updates.
Programming: Python, MATLAB, R, SQL, C/C++, Java, JavaScript, and Mathematica.
Data analysis and visualization: NumPy, pandas, Matplotlib, Tableau, and Excel.
Methods: Statistical learning, kernel methods, optimization, time-series modeling, and numerical experimentation.
Chapman Brain Institute: Research support involving data collection, cleaning, statistical analysis, and visualization.
DATA@UCI: Mentored an undergraduate research team in data analysis, dimensionality reduction, research design, and presentation.