Research and Publications

(Upcoming) Research Interests:

♾️ Partial Differential Equations (PDEs):

• Analysis and Numerical Methods for PDEs and Systems of Hyperbolic Conservation Laws,
• Applications of Systems of Hyperbolic Conservation Laws and Hyperbolic Balance Laws to Fluid Dynamics and Traffic Flow Networks,
• Finite-time Singularities arising from PDEs,
• Mathematical General Relativity (on the Weak Cosmic Censorship Conjecture).

📊 Statistics and Machine Learning:

• Approximation Theory in Machine Learning,
• Physics-Informed Machine Learning and Learning Hidden Systems of Conservation Laws.

Publications:

📜 A Proof of Weak Cosmic Censorship Conjecture for the Spherically Symmetric Einstein-Maxwell-Charged Scalar Field System
       with Xinliang An.
       arXiv:2402.16250 (2024).
       Tags: Analysis of PDEs, General Relativity.

📜 Regularization of Complex Langevin Method
       with Zhenning Cai and Yang Kuang.
       Phys. Rev. D 105, 014508 (2022).
       Tags: Computational Physics, Numerical Analysis.

📜 Hierarchical Bayesian Thermonuclear Rate for 7Be(n,p)7Li Big Bang Nucleosynthesis Reactions
       with Rafael S de Souza, Alain Coc, and Christian Iliadis.
       The Astrophysical Journal 894, 132 (2020).
       Tags: Bayesian Statistics.

You can access my Google Scholar here.