Biography

I grew up in East China, in a beautiful village in the county of Huzhou, Zhejiang Province, which is close to Shanghai.  I read Mathematics in Huzhou’s Teacher’s School, and got my Ph. D. degree in mathematical statistics at the East China Normal University, Shanghai, China. I came to England as Royal society visiting research fellow at Warwick, and lectured at Imperial College London. I joined the National Centre for Scientific Research (CNRS, France) as a senior researcher, and I came back England and joined University of Oxford in 2004 as University Lecturer and Official Fellow at Exeter College.

I have wide interests from mathematics, mathematical physics, quantitative finance to machine learning.

Research

I have been working on problems arising from probability, statistical mechanics and stochastic modelling, a research area called broadly in stochastic analysis: diffusion processes, rough path analysis and machine learning, backward stochastic differential equations and stochastic (partial) differential equations. My research can be applied to some practical questions in financial innovations such as active portfolio management, high-frequency data analysis.

I am also very keen in learning and doing research on mathematical physics such as quantum fields, high energy physics and theoretical aspects of neutrinos.

Teaching

At Exeter, I teach pure and applied papers for students reading in mathematics and mathematics and joint schools, and I teach the topics including analysis, probability, statistics, some physics topics such as relativity and quantum physics.

In Mathematical Institute I lecture the courses Lebesgue Integration, Martingales with Measure Theory, for students reading the papers for the degree of MMath and CDT for Non-linear Analysis of Partial Differential Equations.

Selected Publications

1.    (with T. Lyons) System Control and Rough Paths. Oxford Mathematical Monographs, Clarendon Press, Oxford (2002).

2.    (with Y. Hu and Z. Zhang) Gradient estimates for porous medium and fast diffusion equations by martingale method. Ann. Inst. H. Poincaré Probab. Statist.

3.    (with H. Boedihardjo, X. Geng) Quasi-sure Existence of Gaussian Rough Paths and Large Deviation Principles for Capacities, in Osaka J. of Math.

4.    (with Xi Geng, Danyu Yang)  (arXiv:1306.2021) G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion. Séminaire de Probabilités XLVI, Volume 2123 of the series Lecture Notes in Mathematics pp 125-193.

5.    (with Ying Hu) BMO martingales and positive solutions of heat equations. Mathematical Control and Related Fields, Pages: 453 – 473, Volume 5, Issue 3, September 2015.

6.    (with X. Geng) On an inversion theorem for Stratonovich’s signatures of multidimensional diffusion path. Ann. Inst. H. Poincaré Probab. Statist. Volume 52, Number 1 (2016), 429-447.

7.    (with Xun Yu Zhou)  Existence of Solutions to a Class of Indefinite Stochastic Riccati Equations. SIAM J. Control Optim., 51(1), 221–229. DOI:10.1137/120873777.

8.    (with Yves LeJan) (arXiv:1102.3601) Stratonovich’s Signatures of Brownian Motion Determine Brownian Sample Paths. Probab. Theory Relat. Fields (2013) 157: 209. doi:10.1007/s00440-012-0454-z, Volume 157, Issue 1, pp 209–223.