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Data hiding or steganography in image is a scheme of hiding the secret message into the cover image. It can be used to transmit the secret data by the cover image or embed important information such as copyright information, authentication information or management information in the cover images. The quality of stego-image is the main object of the applications in copyright protection and the image authentication. The method to improve the quality is to enhance the embedding efficiency. In order to achieve a higher embedding capacity and embedding efficiency,

The projective characters of the symmetric group was studied by I. Schur in his seminal paper of 1911, where the famous Schur Q-functions were defined and a Frobenius type character table was established. I. Frenkel, W. Wang and I have generalized Schur's work and computed major part of spin characters of the wreath products in 2001. I will discuss how to compute the missing part of spin characters for the wreath products.

In this work, we introduce {\em topological representations of a quiver} as a system consisting of topological spaces and its relationships determined by the quiver. Such a setting gives a natural connection between topological representations of a quiver and diagrams of topological spaces. First, we investigate the relation between the category of topological representations and that of linear representations of a quiver via $P(\Gamma)$-$\mathcal{TOP}^o$ and $k\Gamma$-Mod, concerning (positively) graded or vertex (positively) graded modules. Second, we discuss the homological theory of topological representations of quivers via $\Gamma$-limit $Lim^{\Gamma}$ and using it, define the homology groups of topological representations of quivers via $H_n$

In this talk I shall report a joint work with Xiao Wei on the graded decomposition numbers and inverse graded decomposition numbers for parabolic Verma modules in any integral blocks of a parabolic category of a semisimple Lie algebra. A sum formula for the radical filtrations of parabolic Verma modules is also obtained, which generalizes the classical Jantzen sum formula for the usual Verma modules.

We investigate the contracting curvature flow of closed, strictly convex axially symmetric hypersurfaces in R^n+1 and S^n+1 by sigma_k^\alpha, where \sigma_k is the k-th elementary symmetric function of the principal curvatures and \alpha\ge 1/k. We prove that for any n\geq3 and any fixed k with 1\leq k\leq n, there exists a constant c(n,k)>0 such that if \alpha lies in the interval [1/k,1/k+c(n,k)], then we have a nice curvature pinching estimate involving the ratio of the biggest principal curvature to the smallest principal curvature at every point of the flow hypersurface, and we prove that the properly rescaled hypersurfaces converge exponentially to the unit sphere. Our results provide an evidence for the general convergence result without initial curvature pinching conditions.

In this talk we will study the limit of a sequence of harmonic maps from surfaces with uniformly bounded energy. We define the generalized neck domain as the union of ghost bubbles and necks that are directly connected and give a uniform upper bound of the energy density on the generalized neck domain. As an application, we prove an inequality of the index and nullity of the sequence.

The i-quantum groups are certain quantum algebras arising from the study of quantum symmetric pairs. They are defined by generators and relations and are embedded as coideal subalgebras of the quantum linear groups. Moreover, the restriction of the famous quantum Schur-Weyl duality pair for quantum linear groups and Hecke algebras of type A gives a duality pair for an i-quantum group and the Hecke algebras of type B. This new duality was discovered by H. Bao and W. Wang. Moreover, Bao, Kujawa, Li and Wang developed a geometric setting of the duality, including some fundamental multiplication formulas and the modified i-quantum group. In this talk, I report a new realization for the i-quantum group $U^j(n)$ and it’s applications to representations of finite orthogonal groups. This is joint work with Yadi Wu.

研究生和大学生的差别是什么？研究生应具备怎样的素质？从大学生到研究生的过程就是从学习到研究、从集体到个体的过程。当一名研究生，要做好充分的准备，要有良好的心态。报告人根据自己三十多年来指导研究生的经验，结合个人成长经历，谈谈研究生阶段应该重视的方面，对研究生的成长提出建议。