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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.

Let Y be a smooth projective surface defined over an algebraically closed field k with char k>2, and let $/pi:X->Y$ be a double covering branched along a smooth divisor. We show that the tangent bundle T_X is stable with respect to $/pi^*{H}$ if the tangent bundle T_Y is semi-stable with respect to some ample line bundle H on Y.

Many computational science and data analysis techniques lead to optimizing Rayleigh-Quotient (RQ) and RQ-type objective functions,such as computing excitation states (energies) of electronic structures,robust classification to handle uncertainty and constraineddata clustering to incorporate a prior information. In this talk,we will discuss origins of RQ optimizations, variational principles,and reformulations to algebraic eigenvalue problems. We will show how to exploit underlying properties of eigenvalue problems for design reliable and fast eigensolvers, and illustrate the efficacy of these eigensolvers in electronic structure calculations and constrained image segmentations.