Ryan Divan

I am a third-year undergraduate in Mathematics at Princeton University, pursuing minors in Computer Science and Applied Mathematics. I have strong interests in numerical analysis, probability, and machine learning. Right now, I'm working on human-AI reasoning in mathematics with the UCLA expMath group and researching randomized algorithms in numerical analysis under Professor Marc Gilles.

Email  /  GitHub  /  LinkedIn

Current Research

Projects that I am currently working on, including those that are unpublished or in progress.

expMath: Scalable Collaborative Human-AI Reasoning in Mathematics

I am working with the UCLA expMath group to develop robust mathematical reasoning models that can support effective human-AI collaboration and build interactive reasoning tools, with a special emphasis on formal theorem proving in Lean.

Randomly Pivoted LU Factorization

I am researching extensions to the theory and implementation of the randomly pivoted LU factorization algorithm, building upon existing work on the algorithm produced in Low-Rank Approximation by Randomly Pivoted LU (Gilles and Wilber, 2026) and the related RPCholesky algorithm in Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations (Chen et al. 2024).

Previous Research

A selection of my longer-term, completed research projects.

Learning to Restart: Reinforcement Learning for Adaptive GMRES(m)

The GMRES(m) algorithm iteratively solves sparse linear systems, typically with a fixed restart parameter m. However, previous work has shown that variable choices of m can lead to stronger convergence behavior. We consider this problem in an online reinforcement learning (RL) framework and propose GMRES-RL, an online RL GMRES(m) algorithm. We find that compressed state-representations of the GMRES(m) residual achieve computational cost and accuracy that is competitive with fixed policies.

Radiative Transport Equation

This project focuses on numerical solutions to the integro-differential radiative transport equation, modeling interial confinement fusion. We proved the well-posedness of the problem and developed a cross-sectional solver using the Streamlined Upwind Petrov-Galerkin (SUPG) and the discrete ordinates method.

Randomized Kernel Approximation for the Diagonal-weighted Generalized Method of Moments (DGMM)

In this reading program, under Liu Zhang, I studied low-rank kernel approximation methods, particularly in the context of Gaussian mixture models. Considering the context provided on DGMM in Zhang’s paper, we prove and empirically verify high-probability asymptotic bounds on the error of various Nyström approximation schemes for matrices relevant to DGMM.

Randomly Pivoted Cholesky: Investigation and Applications

I implemented the RPCholesky algorithm based on the paper by Chen et al. (2022), exploring its applications in kernel learning, image classification, and potential applications to Hankel matrices in the FlashSTU paper by Liu et al. (2025).

Combating Malaria: A Drug Discovery Approach Using Thiazole Derivatives Against PfPKG Enzymes

This study involved the synthesis of six thiazole-derived amides to inhibit the PfPKG pathway, a key part of the malarial Plasmodium parasite life cycle. I led the key efforts of in silico analysis, simulating drug docking in UCSF Chimera and AutoDock Vina. Our research was conducted at the New Jersey Governor’s School in the Sciences and supported by organizations including Novartis and the Overdeck Foundation.

Ventures

A selection of my entrepreneurial ventures and projects.

EVAL Gaming: Connecting Esports Athletes to Scholarships

With Sekou Roland and Ibraheem Amin, I founded a data analytics-driven venture to bring standardized evaluation metrics to high school esports,. I have led development Rocket League, Super Smash Bros. Ultimate, and Valorant status using developer and community APIs. Our clients include the U.S. Military Academy at West Point and Garden State Esports, and we have been awarded grants by the Keller Center and Princeton Student Ventures.

Kachi: Understanding Your Skincare Spend

Alongside Dr. Bryan Quoc Le at Mendocino Food Consulting , I developed Kachi, an app that used a proprietary scoring algorithm based on bioactivity and publications to rank consumers’ skincare products across three main categories: efficacy, value, and markup. I brought the app from a spreadsheet to a web app, incorporating RAG for more effective scanning and analysis, and we ultimately exited to a client.

Coursework

• MAT335: Complex Analysis
• ORF526: Probability Theory
• MAT429: Topics in Analysis: Introduction to Incompressible Fluid Dynamics
• MAT478: Topics in Combinatorics: The Probabilistic Method
• MAT321: Numerical Analysis and Scientific Computing
• MAT380: Probability and Stochastic Systems
• MAT345: Algebra I
• MAT217: Honors Linear Algebra
• MAT215: Real Analysis
• Point Set Topology (Johns Hopkins University CTY, 2022)

• COS585: Information Theory
• COS435: Reinforcement Learning
• COS226: Data Structures and Algorithms
• COS126: Introduction to Computer Science
• PHY210: Experimental Physics Seminar
• ECO310: Mathematical Microeconomics
• FRS113: The Science of Composting
• Cellular Automata (NJ Governor's School in the Sciences, 2023)

• LAT338: The Satyrica of Petronius
• SLA330: Kierkegaard and Dostoevsky
• WRI191: Seeing is Believing
• ATL495: Epistolary Writing
• EGR395: Venture Capital and the Finance of Innovation
• EGR380/381: eLab Startup Incubator
• Global Bioethics and Human Rights (St. Peter's University, 2023)

Design and source code from Leonid Keselman's Jekyll fork of Jon Barron's website