Stochastic multiscale modeling has become a popular approach to quantify uncertainty in multiscale models. The combination of multiscale features and complex uncertainty in models leads to great challenge to simulate the models and explore the propagation of uncertainty. To treat the difficulty, it is desirable to construct a sparse representation for the outputs of the multiscale models. In the talk, we present a sparse representation based on reduced multiscale basis methods and investigate uncertainty quantification for some porous media applications.

We consider the optimal dividend payment strategy for an insurance company, having two collaborating business lines, where their surplus processes are modelled by diffusion processes and the dividends paid by different business lines are weighted differently. We find the optimal dividend strategy when money is transferred between two business lines without transaction costs. We show the optimal value function is the unique continuous viscosity solution to the corresponding HJB equation when money is transferred with transaction costs. We also prove a verification theorem. Finally, we find the optimal solution to the problem with transaction costs in the symmetric case.

We consider the optimal investment and consumption decision of a CRRA investor who is facing capital gains tax and receives labor income. Assume that the investor cannot borrow against future labor income. We investigate how the coexistence of capital gains tax and uninsurable labor income affects the investment and consumption decision. This work is jointly with Yaoting Lei and Hong Liu

Due to the lack of separation principle, the problem of output feedback stabilization for nonlinear systems has been known as a challenging problem. This talk will sketch the recent efforts in solving this problem for several classes of nonlinear systems. The specific topics will cover: continuous-time output feedback control; finite-time output feedback control; sampled-data output feedback control; output feedback control of linearly uncontrollable systems; and applications to some practical systems. Dr. Chunjiang Qian received his B.S. and M.S degrees in Control Theory from Fudan University in 1992 and 1994 respectively, and the Ph.D. degree in Electrical Engineering from Case Western Reserve University, 2001. Since August 2001

Buffon投针是随机几何的一个经典范例。为了研究几何体的随机现象，几何元素集的测度是最基本的问题。本报告将介绍直线集等几何元素集的运动密度、经典等周不等式的Blaschke证明以及Poincaré公式、Blaschke运动基本公式等

The classical isoperimetric problem was known in the Ancient Greek. But the rigorous mathematical proof appeared late till the 19th century. Late works showed that the isoperimetric inequality was equivalent to the analytic Sobolev inequality. Is there an analytic inequality that is equivalent to the Brunn-Minkowski equality? We will discuss this problem.

This paper considers a class of bistable reaction-diffusion equations in the plane. We will focus on the multiplicity, shape and attractivity of the heterogeneous steady states for bistable reaction-diffusion equation in the plane.

题目：The Applications of Tensor Eigenvalues, Positive Semi-Definite Tensors and Copositive Tensors in Physics.报告人：祁力群教授 香港理工大学时间: 2016年12月6日(周二)下午16:00地点: 致远楼107室祁力群教授简介：中国著名数学家。男，江苏扬州人，1984年毕业于美国威斯康星大学计算机科学系，获博士学位。现任香港理工大学应用数学系教授，博士导师。是澳大利亚Curtin科技大学研究教授，俄罗斯Petrovskaya 科学与艺...