Dr. Zhongmin QIAN

https://people.maths.ox.ac.uk/qianz/

I am a University Lecturer in the Mathematical Institute, Oxford, and Fellow at Exeter College. 

Mailing Address: Mathematical Institute, University of Oxford, 24 - 29 St Giles\', Oxford OX1 3LB, UK

Office: Math Institute S7

Tel: (01865) 273 563 (Institute),  (01865) 279 643 (College)

Email: qianz@maths.ox.ac.uk

Research Interests

I specialise in two different research areas: stochastic analysis, and non-linear partial differential equations coming from geometry.

Stochastic Analysis: Nowadays it is difficult to describe broad areas that the research in Stochastic Analysis covers. I am interested in mathematical models for random phenomena, called stochastic processes. A typical example of such processes, that has rich mathematics, is the well-known model for random movements observed by R. Brown, Brownian motion (also called Wiener process). A century ago, a French mathematician L. Bachelier in his thesis studied the mathematical model for stock markets via Brownian motion, and his ideas had been enforced over the past years, and had led to the famous Black-Scholes model for option pricing. My own research in recent years concentrate on

Geometric Analysis. I find myself great fun with the Ricci curvature and its complex companion the first Chern class determined by a complex structure. I am mainly interested in analysis aspects of the Ricci curvature and complex structures, in particular, those (non-linear) partial differential equations (PDE) related to the Ricci curvature and the first Chern class.

1. Harnack\'s inequality.

2. 1-dimensional models for Riemannian spaces.

3. Ricci flow. In the past few years, there are exciting and major progresses in the study of Ricci flows and its application in geometry and topology, especially the substantial contributions made by G. P