赵宇轩 (Yuxuan Zhao)

PhD Candidate in Mathematics | University of Illinois Urbana-Champaign

Research Interests

I am currently working with Professor Daniel B. Cooney at the Univeristy of Illinois Urbana-Champaign. I am currently exploring research questions related to Mathematical Biology.

1. Pattern Formation

I am interested in pattern formation in nonlinear PDEs. In many systems, spatial patterns emerge when a homogeneous equilibrium loses stability, allowing small spatial perturbations to grow and develop into organized structures. My research explores pattern formation driven by different mechanisms in a variety of PDE and nonlocal models, with particular emphasis on stability and bifurcation analysis.

Simulation of pattern formation from a perturbed homogeneous state

2. Multi-Agent Learning and Collective Dynamics

I am interested in understanding how learning, decision-making, and interactions among autonomous agents give rise to emergent collective behavior. In particular, I study how reinforcement learning and other adaptive learning mechanisms can be incorporated into mathematical models of interacting populations, with applications to evolutionary games or mathematical biology.

3. Numerical Methods and Simulations

I am interested in numerical methods and simulations for dynamical systems and PDEs defined on different spatial structures. These include dynamical systems on graphs, PDEs on regular Euclidean domains, and nonlocal evolution equations on graphons.

Publications & Preprints

(* $=$ first author, † $=$ co-first author)

  1. The Keller-Segel Model for Chemotaxis on Metapopulation Graphs and Graphons.
    Daecheol Kim, Yefei Zhang, Yuxuan Zhao†, and Daniel B. Cooney.
    arXiv preprint, arXiv:2610.31049 (2026).

  2. Spatial Pattern Formation from Multi-Agent Learning in Public Goods Dilemmas.
    Yefei Zhang and Yuxuan Zhao.
    arXiv preprint, arXiv:2610.12321 (2026).

  3. 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, 173 (2026). [Journal]

Talks & Conferences

Poster presentation, Evolutionary Games: Mathematical Theory and Biological Insights, National Institute for Theory and Mathematics in Biology (NITMB), Chicago, May 2026.