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.

Calogero-Sutherland模型是一个一维的量子多体完全可积系统。Navier-Stokes方程是流体力学中最基本的微分方程。我们将讲解超几何函数与Calogero-Sutherland模型的联系，并介绍Navier-Stokes方程的对称变换群，非对称解法和活动标架解法

Recent advances in networking technologies, especially wireless networks, generate a new paradigm of control and filtering for industrial systems via networks. Traditionally, such systems are controlled and estimated by independent networks, which are designed with enough bandwidth and resources. In network environments, shared wired and wireless networks are utilized to connect industrial systems and controllers/filters. In this new framework, bandwidth and resource constraints should be taken into account in controller/filter design, and real-time becomes increasingly important to control and filtering.

We introduce a new family of symmetric functions via the Jacobi-Trudi identity to cover the orthogonal or symplectic Schur functions as well as the Okounkov-Olshanski shifted symmetric functions. It is proved that they all can be treated as the usual Schur functions, and their vertex operator realization and Giambelli identities are given by using the boson-fermion correspondence.