Through studying two questions on average subtree orders, we provide some insights on how `dense' or `sparse' a tree can be in this setting. Some characteristics of the dense and sparse trees will be presented. We also briefly mention results on `indistinguishable' graphs/trees that, among many graph invariants, possess the same subtree polynomials. Students are particularly welcome. These studies are inspired by Jamison's early papers and are joint work with S. Wagner and A. Vince.

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