Education
Iowa State University
B.S. Mathematics
Expected May 2027
Cumulative GPA: 3.85/4.00 · Mathematics GPA: 3.89/4.00
In progress · Fall 2026
- MATH 5010 — Introduction to Real Analysis
- MATH 5540 — Stochastic Process Models
Planned · Spring 2027
- MATH/STAT 6450 — Advanced Stochastic Processes
- MATH 5250 — Numerical Analysis of High-Performance Computing
- IE 3120 — Optimization
Selected coursework · Completed
- MATH 3850 · Introduction to Partial Differential Equations
- MATH 4030 · Intermediate Abstract Algebra
- MATH 4430X · Introduction to Mathematical Finance
- MATH 3010 · Abstract Algebra I
- MATH 3170 · Theory of Linear Algebra
- MATH 2660 · Elementary Differential Equations
- MATH 2010 · Introduction to Proofs
- MATH 4900 · Independent Study, 6 credits
Research Experience
Degenerate Diffusions in Finite and Infinite Dimensions: Smoothing and Convergence
Student Researcher · Advisor: David P. Herzog
Summer 2026–Present
NSF-funded research · Award DMS-2246491
- Develop quantitative finite-time Gaussian-approximation results for displacement in periodic Langevin dynamics.
- Proved a one-dimensional Berry–Esseen estimate with Kolmogorov error bounded by C/√(γT), identifying γT as the effective relaxation scale.
- Use measure-theoretic probability, Lp moment estimates, Markov-additive processes, semigroup mixing, martingale methods, and diffusion limits.
- Implemented Python numerical experiments for Langevin dynamics and effective-diffusion estimation.
Nonlinear MBS Pricing Models
Student Researcher · Advisor: Rana D. Parshad
2026–Present
- Study whether stochastic perturbations and nonlinear p-Laplacian diffusion improve the predictive performance of an MBS pricing equation.
- Reconstructed analytical arguments for weak solutions and p-diffusion extensions from the research literature.
- Built an initial backtesting workflow with real transaction data and conducted numerical and financial interpretation of selected model regimes.
- Current direction: stochastic analysis, mean-square sensitivity, noise-driven simulation, and model-risk interpretation.
Random Matrix Theory and Quantum Expanders
ISmART Research Project · Advisor: Jananan Arulseelan
Spring 2026–Present
- Study Haar-distributed unitary matrices, malnormal matrices, commutator lower bounds, and quantum expanders.
- Developed numerical experiments on non-normal spectral behavior and pseudospectra.
- Produced a technical note on Haar random unitaries, commutator bounds, and pseudospectral behavior.
Manuscripts
In Progress
Berry–Esseen Bounds for Periodic Langevin Dynamics
In Progress
Prediction, Model Risk, and Stochastic Sensitivity in Nonlinear MBS Pricing Models with p-Laplacian Diffusion
Directed Studies
Four faculty-guided studies form the analytical preparation behind my work in stochastic dynamics, probability, PDE, and mathematical finance.
David P. Herzog
Stochastic Calculus
Text: Bernt Øksendal, Stochastic Differential Equations: An Introduction with Applications, 6th ed.
Brownian motion, Itô integration and formula, SDEs, diffusion generators, and stochastic dynamics.
Ruoyu Wu
Foundations of Probability
Text: Ross and Leadbetter, A Basic Course in Measure and Probability.
Measure-theoretic probability, random variables, integration, independence, and modes of convergence.
Ruoyu Wu
Real Analysis and Measure Theory
Text: H. L. Royden and P. M. Fitzpatrick, Real Analysis, 4th ed.
Lebesgue measure and integration, convergence theorems, and Lp spaces; these tools are used extensively in my stochastic-dynamics research.
Rana D. Parshad
Partial Differential Equations I
Text: Lawrence C. Evans, Partial Differential Equations.
Sobolev spaces, weak derivatives and solutions, and functional-analytic methods for PDE.
Honors & Awards
Athletics
Iowa State University Men’s Golf
NCAA Division I Student-Athlete
August 2023–Present
- Represent Iowa State University in NCAA Division I tournaments.
- Balance more than 20 hours of weekly training and competition with a full mathematics course load.
- Best World Amateur Golf Ranking: 443.
Technical Skills
- Programming
- Python, MATLAB, C (currently learning)
- Scientific work
- Numerical simulation, stochastic-process simulation, market-data analysis
- Typesetting
- LaTeX
- Languages
- English (fluent); Mandarin and Hakka (native)