In this talk, we present a method to analyze certain fast-slow motions in dynamical systems. For singular perturbed dynamical systems, the well-known Geometric Singular Perturbation Technique (GSPT) is usually applied to find the special limit cycles -- fast-slow periodic solutions. However, many practical problems may not be able to be put in the form of singular perturbed equations, but they still exhibit fast-slow motions. In that case, based on dynamical system theory

In this talk, I will give the Agmon-type estimates of Bergman kernels under the conditions of the curvature or the Ricci curvature bounds. This is joint work with Shoo Seto

Singular elliptic equations have been the target of investigation for decades. A very nice result for existence of solutions of such an equation is due to Lazer-McKenna [Proc.AMS 111(1991)]. In that paper the Lazer-McKenna obstruction was first presented: the equation has a solution if and only if –p>-3. In this talk we reveal the role of -3: why -3 is so crucial for elliptic equations with negative exponents. Then I shall talk about some about $L_{p}$ Minkowski problem with negative exponents $p$.

We develop a general equilibrium model of exhaustible resources with production adjustment costs based on singular control, and show that the classical Hotelling’s rule, which states that the prices of the exhaustible resources should grow at the risk-free rate, does not hold in the presence of adjustment costs; indeed, the adjustment costs can lead to a U-shaped price profile, while will significantly prolong the period of price staying at the bottom.

题目：Mathematical Analysis of Credit Default Swap报告人：陈新富 教授 (匹兹堡大学)时间：2017年5月5日(星期五) 下午2：00—3：00地点：致远楼107室欢迎各位参加

介绍全纯曲线在角域上的各类特征及基本定理，并介绍这些基本定理在奇异方向和唯一性方面的应用

In this talk I will introduce Deligne-Illusie's algebraic proof of the Kodaira vanishing theorem and the E1 degeneracy theorem of the Hodge-de Rham spectral sequence. The decomposition theorem of Deligne-Illusie is the key to the proof mentioned. To understanding the Hodge theory of degenerated varieties over a positive characteristic field, Illusie posts a problem of decomposability of the log de Rham complex in the case of semistable reduction.

A conical conformal metric is a Hermitian metric on a Riemann surface with constant Gaussian curvature and isolated conical singularities. A fundamental problem of such metrics is whether there exists a conical conformal metric for any given prescribed singularities. In this talk, I will give a construction of conical conformal metric with positive constant curvature by a given Strebel differential. Then I will present a generalization of a well-known existence theorem by Kurt Strebel. As a consequence, we obtain an existence result for a new class of conical conformal metrics on Riemann surfaces.