In this work, we study the finite element approximation of a free boundary plasma problem, which is related to some problems in electromagnetics. Using a mixed approach (which resembles an optimal control problem with control constraints), we formulate a weak formulation and study the existence and uniqueness of a solution to the continuous model problem. Using the same setting, we formulate and analyze the discrete problem. We derive optimal order energy norm a priori error estimates proving the convergence of the method.Further,

This talk concerns the minimization problem of $L^2$ norm of curl of vector fields in multiconnected bounded domains prescribed full trace on the boundary. The existence and $H^2$ estimate of the minimizers are established.

In this seminar, a novel approach is presented for control design with guaranteed transient performance for multiple-input multiple-output discrete-time linear polytope difference inclusions. We establish a theorem that gives necessary and sufficient conditions for the state to evolve from one polyhedral subset of the state-space to another. Then we present an algorithm which, given a time-varying polyhedral set called the target tube, which may be specified from typical transient performance specifications, constructs an output feedback law that guarantees that the state evolves in this tube.

We study small covers and the real moment-angle manifold over a simple polytope that admit Riemannian metrics of positive scalar curvature. We first explain some general facts on the existence of positive scalar curvature on a smooth manifold.Then we show a class of simple polytopes over which the small covers and the real moment-angle manifolds

In this talk, I will introduce a possible way to consider the cabling conjecture from the view of Heegaard splitting.

Let M be a unitary closed manifold that admits an action of a circle preserving the unitary structure and fixing some isolated points. Kosniowski conjectured in 1980 that if M is not a boundary, then the number of isolated points is at least [dim M/4]+1. This talk will discuss different statements of Kosniowski conjecture and state some recent progresses.

Positive mass theorem is one of the most fundamental results in both physics and mathematics. It has many applications in various fields of geometric analysis. As its compact manifold version, the positive mass theorem for Brown-York mass has been also proved to be a very powerful tool in the study of geometry. In this talk, we will briefly review the positive mass theorem due to Schoen-Yau-Witten and Brown-York mass theorem due to Shi-Tam. As applications of Shi-Tam's result, we show how to use it to derive some interesting geometric results such as estimates of first eigenvalue of Laplacian with scalar curvature positively lower bounded and an area estimate of critical set for Besse's conjecture etc.

题目：Integer Flows of Cayley Graphs报告人：张存铨 教授 （West Verginia University）时间：2018年6月9日上午10:00地点：致远楼101室欢迎大家前往听讲