Research & Projects

I work in stochastic analysis and probabilistic treatments of gas dynamics, namely the Boltzmann equation. I examine stochastic processes whose laws are driven by kinetic equations and determine properties of these probability distributions. Other interests of mine are machine learning, stochastic neural networks, probabilistic number theory, martingale problems, and financial applications of stochastic analysis.

For projects I've advised, they have mainly focused on mathematical modelling, probability theory, analysis or machine learning. 

1. (with Barbara Rüdiger and Padmanabhan Sundar) Density valued solutions for the Enskog process. (in preparation)

2. (with Lisa Kuhn, Kaleb Champagne, & Keaton Pierson). Quintic and biquintic B-spline finite element solutions of clamped structures. International Journal for Computational Methods in Engineering Science and Mechanics, 1–12. 2024.

3. (with Kaleb Champagne and Lisa Kuhn) Modified Bi-Cubic and Bi-Quintic B-Spline Basis Functions for Simulating a Thin Plate Structure. Proceedings of the International Conference on Scientific Computing (CSC). 2019.

4. (with Andrew Sievers, Lisa Kuhn, and Steele Russell) An analysis of MATLAB's software performance interfaced with high-level C language for expediting numerical integration technique. Consortium for Computing Sciences in Colleges 33, 4. 2018.

5. (with William Holland, Omer Mujawar, Aadit Narayanan, Frank Neubrander, Marie Neubrander, and Christina Simino) Words in Random Binary Sequences I. arXiv. (preprint) 2021.

Here are some projects I've mentored or otherwise assisted with as a TA. These are all either at a high school or undergraduate level. Links are provided to either the project summary, slides, or poster where applicable.

Spring 2024: Multiclass Machine Learning for Frog Egg Image Classification. The slides have not yet been posted. This project began the expansion of a machine learning model for counting frog eggs. The end goal is to both count and classify frog eggs at different stages in their life cycle. 

Fall 2023: Aquaponic Deep Water Systems

Summer 2022: Completeness of Distributions

Summer 2021: Dictionary Probabilities and Probabilities on the Integers

Summer 2020: Words in Random Binary Sequences. There are not slides or a poster available online for this project. However, there is a preprint paper available on arXiv.