Currently an Visiting Assistant Professor at the University of Massachusetts Amherst. I am now on the job market and I am actively looking for a tenure-track position (in applied mathematics and/or related areas) starting at Fall 2025. Hobbies: Naruto/Boruto, Detective Conan, NBA, Yu-Gi-Oh! (a trading card game, I am a semi-professional Yu-Gi-Oh! player by the way), etc. Email: fcao@umass.edu. I am glad to discuss mathematics and potential research collaboration possibilities with you via email. I am interested in partial differential equations, stochastic processes, interacting particle systems, and theoretical machine learning. My Ph.D advisor is Sebastien Motsch. My CV can be found at here. Please always refer to my Google Scholar or Curriculum Vitae for my up-to-date publications and pre-prints.

Publications

• Asymptotic flocking for the three-zone model; Mathematical Biosciences and Engineering, 17(6):7692-7707, 2020; Fei Cao, Sebastien Motsch, Alexander Reamy, Ryan Theisen.
• K-averaging agent-based model: propagation of chaos and convergence to equilibrium; Journal of Statistical Physics, 184(2):1-19, 2021; Fei Cao.
• Explicit decay rate for the Gini index in the repeated averaging model; Mathematical Methods in the Applied Sciences, 46(4):3583-3596, 2023; Fei Cao.
• Derivation of wealth distributions from biased exchange of money; Kinetic and Related Models, 16(5):764-794, 2023; Fei Cao, Sebastien Motsch.
• Entropy dissipation and propagation of chaos for the uniform reshuffling model; Mathematical Models and Methods in Applied Sciences 33(04):829-875, 2023; Fei Cao, Pierre-Emmanuel Jabin, Sebastien Motsch.
• Uncovering a two-phase dynamics from a dollar exchange model with bank and debt; SIAM Journal on Applied Mathematics, 83(5):1872-1891, 2023; Fei Cao, Sebastien Motsch.
• Uniform propagation of chaos for a dollar exchange econophysics model; European Journal of Applied Mathematics, 1-13, 2024; Fei Cao, Roberto Cortez.
• From the binomial reshuffling model to Poisson distribution of money; Networks and Heterogeneous Media, 19(1):24-43, 2024; Fei Cao, Nicholas F. Marshall.
• From interacting agents to Boltzmann-Gibbs distribution of money; Nonlinearity, 37(12):125020, 2024; Fei Cao, Pierre-Emmanuel Jabin.

Submitted papers

• A biased dollar exchange model involving bank and debt with discontinuous equilibrium; Submitted, 2023; Fei Cao, Stephanie Reed.
• On the equivalence between Fourier-based and Wasserstein distances for probability measures on N; Submitted, 2024; Fei Cao, Xiaoqian Gong.
• Sticky dispersion on the complete graph: a kinetic approach; Submitted, 2024; Fei Cao, Sebastien Motsch.
• Quantitative convergence guarantees for the mean-field dispersion process; Submitted, 2024; Fei Cao, Jincheng Yang.
• Fractal opinions among interacting agents; Submitted, 2024; Fei Cao, Roberto Cortez.
• The iterative persuasion-polarization opinion dynamics and its mean-field analysis; Submitted, 2024; Fei Cao, Stephanie Reed.
• From Gini index as a Lyapunov functional to convergence in Wasserstein distance; Submitted, 2025; Fei Cao.

Teaching

• MAT 171 Precalculus (Fall 2019) at Arizona State University
• MATH 132 Calculus II (Fall 2022,2024 and Spring 2023) at University of Massachusetts Amherst
• MATH 331 Ordinary Differential Equations (Fall 2023 and Spring 2024,2025) at University of Massachusetts Amherst
• MATH 131 Calculus I (Fall 2024) at University of Massachusetts Amherst

Miscellaneous

• Visiting Scholar in the in the School of Mathematical and Statistical Sciences at Arizona State University (11/06/2023 - 11/10/2023), hosted by Associate Professor Sebastien Motsch.
• Visiting Scholar in the Department of Mathematics at the Pennsylvania State University (02/02/2022 - 02/18/2022), hosted by Professor Pierre-Emmanuel Jabin.
• REU mentor during summer 2023, the undergraduate mentee Minh Le is guided to work on gradient descent and related optimization algorithms.
• Graduate Student Research Award (2022) awarded by School of Mathematical and Statistical Sciences at Arizona State University.