During our biological study we came across a new piece of mathematics. We found it extremely useful in study of robustness and stability of biological processes. It has a fundamental connection to the basic structure in physics that we have to take the stochasticity as an essential element to describe nature. We have applied it to various problems in biology, such as gene switch, the genesis and progression of cancer. We have also explored its mathematical implications from theoretical scientist's perspective. In this lecture I would be happy to share with on what we have obtained, and, outlined some open problems.

敖  平 ： 教育部长江学者计划特聘教授、上海交通大学系统生物医学研究院特聘教授、上海大学定量生命科学国际研究中心特聘教授。

References:
1. Potential in stochastic differential equations: novel construction
P Ao.  J. Phys. A: Math. Gen. 37 (2004) L25–L3  
2. Structure of stochastic dynamics near fixed points
Chulan Kwon, Ping Ao, David J. Thouless.  PNAS  102  (2005) 13029–13033
3. SDE decomposition and A-type stochastic interpretation in nonequilibrium processes
Ruoshi Yuan, Ying Tang, Ping Ao.  Front. Phys. 12 (2017) 120201  
4. Global potential, topology, and pattern selection in a noisy stabilized Kuramoto–Sivashinsky equation
Yong-Cong Chen, Chunxiao Shi, J. M. Kosterlitza, Xiaomei Zhu, Ping Ao.  PNAS 117 (2020) 23227-23234