The Yamabe equation is an important class of equations in the geometric analysis and nonlinear elliptic equations. It arises from the conformal geometry and describes the scalar curvatures of the conformal metrics. In this talk, we study asymptotic behaviors of solutions of the Yamabe equation with isolated singularities and discuss some important results by Caffarelli, Schoen, Spruck, Korevaar, Mazzeo and Pacard. We will also present some recent results that solutions near isolated singularities are well approximated by series that decay at discreet orders.

In this talk, I will review a few existing results about Picard groups of moduli spaces of sheaves over curves, as well as the rank 2 case over surfaces. Based on the related methods, I will discuss how to obtain similar results for high rank cases over surfaces. This is work in progress, conducted jointly with Jun Li, Howard Nuer, Xiaolei Zhao and Yi Xie.

In this talk, I will first review a subsets- counting technique, and then present some applications in number theory and coding theory, with a focus on a partial result on the Borwein conjecture. This is based on joint work with Daqing Wan.

我们将给出密码货币体系中数字权益歧视性的定义，并分析歧视性与安全性、歧视性与效率之间的关系，并尽可能详细介绍相关的数学理论。

Exponential sums over finite fields play a fundamental role in number theory, arithmetic geometry and their applica- tions. This talk presents an expository introduction to the p-adic aspects of this subject. Various classical examp- les will be given to illustrate the general theory.

Slim cyclotomic q-Schur algebras were first introduced by Z. Lin and H. Rui, as centralizer subalgebras of Dipper-James-Mathas’ cyclotomic q-Schur algebras. Recent developments allow us to take the investigation to a new level. First, by using the matrix labelling of C. Mak for certain double cosets, we may construct an integral basis, simpler than the cellular basis, for these algebras. Second, the introduction of the Lusztig type form for quantum affine gl_n by Q. Fu and myself allows us to establish the cyclotomic Schur-Weyl duality at the integral level. Finally, when q is not a root of unity, we obtain a classification of irreducible representations. I will also mention some problems and conjectures. This is joint work with B. Deng and G. Yang.

In this paper, q-Gaussian distribution, q-analogy of Gaussian distribution, is introduced to characterize the prior information of unkown parameters for inverse problems. Based on Q-Hermite polynominals, we propase a spectral likelihood approximation algorithm of Bayesian inversion. Convergence results of the approximated posterior distribution in the sense of KullbackpLeibler divergence are obtained when the likelihood function is replaced with the SlA and the prior density function is truncated to its partial sum. In the end, two numerical examples are displayed, which verify our results.