Jian-Guo Liu

Visiting Professor of Mathematics at NYU Shanghai

Email: jg19@nyu.edu 

Jian-Guo Liu is visiting NYU Shanghai for the Spring term 2019. He is a professor of mathematics and physics at Duke University. He works on partial differential equations, kinetic theory, fluid dynamics, numerical analysis, machine learning and particle systems. He is a fallow of AMS and co-editor of Journal of hyperbolic differential equations. He was a Courant Instructor at NYU’s Courant Institute of Mathematical Sciences.

Research Interests

  • Partial Differential Equations, 
  • Kinetic Theory 
  • Numerical Analysis 

Recent Publications

  •  Y. Feng, L. Li and J.-G. Liu, Semigroups of stochastic gradient descent and online principle component analysis: properties and diffusion approximations. Comm. Math. Sci., 16 (2018) 777-789.
  •  P. Degond, J.-G. Liu, and R.L. Pego, Coagulation-fragmentation model for animal group-size statistics, J. Nonlinear Science, 27 (2017) 379–424.
  •  J.-G. Liu and R. Yang, Propagation of chaos for large Brownian particle system with Coulomb interaction, Research in the Mathematical Sciences, (2016) 3:40.
  •  J.-G. Liu and R.L. Pego, On generating functions of Hausdorff moment sequences, Trans. Amer. Math. Soc. 368 (2016) 8499-8518.
  •  P. Degond, A. Frouvelle, J.-G. Liu, Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, Arch. Rat. Mech. Anal. 216 (2015) 63-115.
  •  P. Degond, J.-G. Liu and C. Ringhofer, Large-scale dynamics of Mean-Field Games driven by local Nash equilibria, J Nonlinear Sci., 24 (2014) 93-115.


  • PhD, Mathematics, UCLA, 1990
  • MS, Mathematics, Fudan University, 1985
  • BS, Mathematics, Fudan University, 1982