Yefei Zhang

Ph.D. Candidate in Mathematics · University of Illinois Urbana–Champaign

I am a Ph.D. student in the Department of Mathematics at UIUC, advised by Daniel Cooney. I expect to graduate in May 2027.

My research sits at the interface of nonlinear dynamics on networks, PDEs, and machine learning: continuum (graphon) limits of dynamics on large graphs, pattern formation in spatial evolutionary games and chemotaxis models, and the mathematics of optimization and transport that underlies modern generative models. I also enjoy working on applied problems in quantum computing and scientific vision–language models.

“The whole universe is in a glass of wine.” — Richard Feynman

Publications & Preprints

Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.
Yuxuan Zhao, Kaisheng Zhu, Yefei Zhang, and Daniel B. Cooney.
Bulletin of Mathematical Biology, 88(10), 173, 2026. doi:10.1007/s11538-026-01733-0
RiverONE: Generating Knowledge-Intensive VLM by Simulated Quantum Machines.
Xindian Ma, Xinyu Long, Yefei Zhang, et al.
arXiv:2606.29966, 2026. Outstanding Paper Award — WAICA Workshop on AI-Driven Quantum Computing Acceleration, World AI Conference, Shanghai, Jul 2026.
Success-Driven Migration on Graphs and Graphons: Continuum Limits and Pattern Formation.
Amy Bradu, David (Rui) Sang, Stanley Combes, Yefei Zhang, and Daniel B. Cooney.
Under review, 2026.
The Keller–Segel Model for Chemotaxis on Metapopulation Graphs and Graphons.
Daecheol Kim, Yefei Zhang, Yuxuan Zhao, and Daniel B. Cooney.
Under review, 2025.

Experience

Graduate Fellow · Institute for Pure & Applied Mathematics (IPAM), UCLA

Los Angeles, CA · Mar–Jun 2025

Selected fellow for the semester-long program on non-commutative optimal transport; studied Wasserstein-type metrics for quantum states and operator algebras.
Developed computational methods for entropy-regularized (Sinkhorn-type) transport — the optimization framework underlying modern generative modeling and distribution matching.

Teaching Assistant · Department of Mathematics, UIUC

Urbana, IL · Jan 2022–Present

Taught Calculus, Linear Algebra, and Differential Equations; designed PrairieLearn assignments for 100+ students.

Selected Projects

Numerical Modeling of FKPP on Networks · Illinois Mathematics Lab

Jan–May 2026

Led an undergraduate team building finite-difference solvers for reaction–diffusion (Fisher–KPP) equations on metric graphs; estimated traveling- and spreading-wave speeds on star, bridge, and tadpole topologies.

Symplectic Map Optimization · Illinois Mathematics Lab

Aug–Dec 2025

Led a research team on symplectic map optimization: parameterized map families and applied the Adam optimizer to discover high-efficiency embeddings; benchmarked algorithmic performance across parameter regimes.

Education

University of Illinois Urbana–Champaign

Expected May 2027

Ph.D. in Mathematics (Advisor: Daniel Cooney) · M.S. in Mathematics, May 2023

Colorado State University

2020-2021

B.S. in Mathematics and Chemistry · GPA 4.0/4.0, Summa Cum Laude

East China Normal University

2017–2021

Dual B.S. in Chemistry, Shanghai, China · Exchange student at Belmont University (2019)

Miscellaneous

Outside of mathematics, I am an amateur cook, runner, and traveler.