n this talk, we discuss about a family of a robust nonparametric estimators for a regression function based on the kernel method when the explanatory r.v . are functional. We first recall some basic definition and we state the almost complete convergence of the estimator under the concentration property on small balls probability measure of the functional explanatory variable when the observations are strong mixing. After, we state the asymptotic normality of the constructed estimator in the two cases, iid and strong mixing. We illustrate our methodology by two examples for real data. Finally we give some open questions.

报告人：郭坤宇教授(复旦大学)题目：Operator theoretic analogue for Lehmer’s problem时间：2013年5月27日(星期一)下午4：00—5：00地点：数学系致远楼10

In this talk, we will introduce a class of stochastic differential equations with Levy noise including the motivation, some definition and properties. We propose several sufficient conditions under which we investigate the long-time behavior of the solution including the asymptotic stability in the pth moment and almost sure stability. Also, we discuss two types of continuity of the solution: continuous in probability and continuous in the pth moment. Finally, we provide two examples to illustrate the effectiveness of the theoretical results.

we give an algebra--combinatorics formula of the Mobius transform for an abstract simplicial complex on in terms of the Betti numbers of the Stanley--Reisner face ring of . Furthermore, we employ a way of compressing to estimate the lower bound of the sum of those Betti numbers by using this formula. As an application, associating with the moment-angle complex (resp. real moment-angle complex ) of , we show that the Halperin--Carlsson conjecture holds for (resp. ) under the restriction of the natural -action on (resp. -action on ).

报告人：郭柏灵院士(北京应用物理与计算数学研究所)题目： Low Regularity for the Nonlinear Schrodinger Equations with Derivative时间：2013年5月23日(星期四)上午10：00—11：00地点：数学系致远楼10

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.