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主要介绍多重网格法和区域分解法，以及它们的应用。

学术报告报告人：徐洪坤教授（第三世界科学院院士，台湾中山大学西湾讲座教授）题目: The lasso: Variants and Iterative Methods时间：2014年9月10日(星期三) 下午4：00—5：00地点：数学系致远楼102欢迎各位参加

As shown in classical linear system theory, the behavior of a linear system is determined by its intrinsic structure, but this connection for nonlinear systems has not been clearly identified and utilized. On the contrary, the intrinsic nonlinear structures of a system are indeed often ignored or even destroyed by linearization or feedback linearization methods. Recently, the success of homogeneity based approaches in designing state and output feedback stabilizers has led to renewed interests in this theory. This talk will sketch the recent efforts in revitalizing and advancing homogeneous system theory for analyzing nonlinear characterizations and designing nonlinear controllers. The specific topics will cover: homogeneity based approaches such as adding a power integrator and homogeneous domination approach for output feedback control;

This lecture will present some new results on global stabilization by output feedback for nonminimum-phase nonlinear systems of a cascade configuration that consists of a driven system (inverse dynamics) and a driving system. Although the zero dynamics may be unstable, there exists an output feedback control law, globally stabilizing the nonlinear system, if both the driven and driving systems have a triangular form and satisfy a global Lipschitz-like condition, and the inverse dynamics is input-to-state stabilizable. A controller design algorithm, examples and simulation results are presented to demonstrate the control strategy and its effectiveness. Discussion will be given on control of nonminimum-phase nonlinear systems, a challenging and important open research topic.

我们常常喜欢了解数学的前沿，那里给人的印象都是高深的数学。其实，前沿和高深的数学都是围绕基本问题展开的，很多基本的问题都来自简单的数学。在这个报告中我想用一些例子说明简单的数学其实与高深的数学有着密切的关系，简单的数学能帮助我们认识一些高深和前沿数学的根基是什么

We first explain and justify the connection stated in the title in the setting of type A. Then we develop a new Schur-type duality featuring Hecke algebra of type BC, and use it to initiate a new theory of canonical basis arising from quantum symmetric pairs. This allows us to formulate and establish for the first time the Kazhda-Lusztig conjecture of the ortho-symplectic Lie superalgebras. This is joint work with Huanchen Bao (Virginia).

In quantum information science, quantum gates acting on vector states are unitary transformations. It is descirable from the theoretical as well as practical point of view to decompose a general unitary transformation into simple ones that are easy to control and implement. In this talk, we will describe current research on this topic.

In this talk, I present recent results on singular limits of first-order quasilinear hyperbolic equations with stiff relaxation term in several space dimensions. The limit equations are of parabolic type accompanied by differential constraints. I give physical models to explain this limit. The justification of the limit is shown in a framework of smooth local-in-time solutions under stability conditions.