In this talk, we will first review the background of the sliding mode control (SMC) and justify the motivation for using SMC to solve the estimation/control problems for nonlinear stochastic systems. We will consider the following four cases: 1) SMC with randomly occurring nonlinearities and time-varying delays; 2) H-infinity SMC with stochastic nonlinearities and time-varying delays; 3) SMC with randomly occurring uncertainties, randomly occurring nonlinearities and mixed time-delays; and 4) SMC with mixed time-delays and Markovian jumping parameters. The main theme is the introduction of randomly occurring incomplete information into the SMC design. Both the theoretical research and engineering applications will be discussed, and a series of recently published results will be reported.

In this talk, we will review the subject of Schubert calculus briefly. We will start with a typical question in enumerative geometry, and will introduce the quantum cohomology of flag manifolds, including part of my joint work with Naichung Conan Leung in the research field.

题目：On the Levi flats in Hopf manifolds报告人：Takeo Ohsawa 教授名古屋大学时间：2013年5月3日，15:30--17:00地点：致远楼 105

报告人：魏文宁博士(复旦大学)题目：On the Cauchy Problem for Backward Stochastic Partial Differential Equations in Holder Spaces时间：2013年4月25日(星期四)下午2：00—3：00地点：数学系致远楼10

报告人：张伏博士(复旦大学)题目：Path-Dependent Optimal Stochastic Control and Viscosity Solution of Associated Bellman Equations时间：2013年4月25日(星期四)下午3：00—4：00地点：数学系致远楼10

报告人：应坚刚教授(复旦大学)题目： 关于鞅表示定理时间：2013年4月18日(星期四)下午3：30—4：30地点：数学系致远楼10

报告人：郑惠恒教授（英国帝国理工）题目：Markov Modulated Weak Stochastic Maximum Principle时间：2013年4月11日，星期四下午3：00—4：00地点：数学系致远楼10

报告人：汤善健教授(复旦大学)题目： 路径相关微分系统的最优控制时间：2013年4月11日(星期四)下午2：00—3：00地点：数学系致远楼10

When looking at surfaces in R^3, the most appealing pictures of surfaces frequently show the presence of symmetries. In this talk we will start by discussing the notion of "symmetry" for arbitrary surfaces. We will continue by introducing two types of "moving frames". A characterization of and a construction principle for surfaces of constant mean curvature will follow naturally. Returning to symmetries, we will express them for arbitrary surfaces in terms of certain "orthogonal moving frames".

High-dimensional data pose many challenges to traditional statistical and computational methods. Specifically, due to the small sample size, there are more uncertainties associated with standard estimations of parameters such as the mean and variance estimations. As a consequence, statistical analyses based on such parameter estimation are usually unreliable. To obtain more accurate parameter estimation some statistical methods, such as regularization through shrinkage, may yield better results. In this talk, I will first review some new developments in shrinkage estimation on variances, under the framework of microarray data analysis. I will then introduce a recent work of mine that develops the shrinkage estimation of the population mean under the quadratic loss function for high-dimensional data. For illustration, a shrinkage-based diagonal discriminant rule will be proposed and it will be demonstrated to outperform the existing competitor in a wide range of settings.