Research and Projects

My current research lies in using machine learning and bayesian statistics for analyzing medical data. I am interested in using techniques that involve change of bases, like Fourier transforms or spectral decompositions.

In the past, I had a taste for using creating medical treatment plans using mathematical optimization. Before that, I had a stint in more theoretical mathematics, generating algorithms for problems in computational algebra.

Course projects reflect my desire to blend interesting theory, modern applications, and computational tractability--take a look at some of them!

Fellowships

(2024-29) NSF GRFP
(2024) MINDS Fellowship, JHU
(2022-23) Bradford Fellowship, JHU

Publications

Computing Rational Powers of Monomial Ideals, Pratik Dongre, Benjamin Drabkin, Josiah Lim, Ethan Partida, Ethan Roy, Dylan Ruff, Alexandra Seceleanu, Tingting Tang. Journal of Symbolic Computation, 2023. doi.org/10.1016/j.jsc.2022.08.018.

Graduate Research

Machine Learning for Medical Data Analysis

Mentors: Tamás Budavári (JHU Applied Math and Statistics), Rohan Mathur (JHU School of Medicine)

Analyzing patient data from the ICU at the Neurosciences Critical Care Unit (NCCU).

Undergraduate Research

Mathematical Optimization Approaches to Radiation Therapy Treatments of Brain Metastases

NCSU REU (DRUMS) 2021

Mentors: David Papp, Maria Macaulay.

Ideated and tested large-scale, mixed integer optimization models that assessed the benefits of non-uniformly fractionated treatment plans.

Line Solitons in the Kadomstev-Petviashvili Equations

Brown University

Mentor: Justin Holmer

Coded numerical simulations to investigate the stability of line solitons in KP equations.

Real Power of Monomial Ideals

Polymath Jr. REU 2020

Mentors: Alexandra Seceleanu, Benjamin Drabkin, Tingting Tang.

Designed 3 algorithms that compute the real power of monomial ideals and implemented in Macaulay2.

Class Projects

Sparse Recovery Using Basis Pursuit and Orthogonal Matching Pursuit

Recovered sparse images using probabilistic algorithms. With Justin Bennett and Ryan Pilgrim.

High-dimensional Approximation, Probability, and Statistical Learning, Spring 2023.

Chirp Signal Detection using Wavelets

Designed an algorithm to detect chirp signals masked in random noise.

Wavelets and Applications, Spring 2021.

pdf | code

Knot (dis)equivalence by knot-coloring

15-min lesson on distinguishing between knots using knot-coloring. With Alexander Ivanov.

Topology, Fall 2020.

video

Age-structured Population Models

Group study on Chapter 5.1 of Logan's Applied PDE, 3rd Edition. Plotted numerical solutions for textbook exercises. With Bill Ma, Daniel Park, Jason Senthil.

Applied PDE, Fall 2020.

pdf | code

(video) ~60% - horizontal.mov

Pattern Formation in Sandpile Models

Used computer simulations to investigate symmetries and stability of sandpile avalanches.

Applied Dynamical Systems, Spring 2020.

pdf | images/videos | simulator (p5)

AIvsAIDemo.mp4

Connect 4

Terminal based game of Connect 4, written in ReasonML. Players can be Human or AI. Joint-winner of the class' AI tournament. With Will Chen.

Computer Science: An Integrated Introduction, Fall 2019.