In this lecture, we shall consider the mean field equation as an integrable system. Recently I and my collaborators have developed a theory to study the mean field equation. I will survey a part of this theory and show at the simplest situation how modular forms would be connected with the PDE.

We will discuss three aspects of the application of scientific methods to finance: (1) Investment (2) Derivatives (3) Risk Management. Although more advanced tools, such as stochastic differential equations, Monte Carlo simulation, psychology, statistical inference, optimization, and functional analysis may be needed to study these topics, only high school mathematics will be used in the talk. We aim at giving some concrete examples in these topics, to inspire interests among the general public. In particular, we will focus on three examples: (1) Optimal portfolio choices, e.g. Kelly and Merton criteria. (2) The binomial model for option pricing. (3) Axioms for risk measures.

Introduced by Borcherds, vertex operator algebra is a new algebra object arising from both mathematics and physics. In this expository talk, we will discus the origins and recent developments of vertex operator algebra. In particular, we will present a connection between vertex operator algebras and the modular forms.

Structures of dual Lie bialgebras on the one sided Witt algebra, the Witt algebra and the Virasoro algebra are investigated. As a result, we obtain some new infinite dimensional Lie algebras. This talk is based on a joint work with Yucai Su.

In many medical studies some markers, such as the medical costs incurred during each hospitalisation, are only measured when an event, such as a hospitalisation, occurs. In addition, there may exist an informative terminal event that stops the follow-up. In this article, we propose an additive-multiplicative mean model for marker data contingent on recurrent event with an informative terminal event via latent variables. Estimation procedures are developed for parameter estimation, and asymptotic properties of the proposed estimators are derived. In addition, some numerical procedures are provided for model checking. The finite sample properties of the proposed estimators are examined through simulation studies. An application to a medical cost study of chronic heart failure patients from the University of Virginia Health System is illustrated.

学术报告报告人：汪寿阳研究员（第三世界科学院院士,中科院数学与系统科学研究院）题目: 一个原油价格形成机制的理论与EMD的几个数学问题时间：2014年9月21日(星期日)下午4：30—5：30地点：数学系致远楼107欢迎各位参加

学术报告报告人:章梅荣(清华大学数学系)题目：非退化位势与非线性微分方程解集合的结构时间：2014年9月19日(星期五)上午9：00—10：00地点：致远楼102欢迎各位老师和参加

学术报告报告人:舒洪颖题目：Global dynamics on viral dynamics时间：2014年9月19日(星期五)上午10：00—11：00地点：致远楼102欢迎各位老师和学生参加