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.

With the development of the hardware, the numerical study on the all-electron Kohn-Sham equation has been attracting more and more attention, which potentially would play an important role in studying a variety of physical phenomena such as high harmonic generation. In this talk, towards the efficient numerical solver for the all-electron Kohn-Sham equation, an adaptive finite element framework

We address the following rainbow Ramsey problem: For posets P, Q what is the smallest number n such that any coloring of the elements of the Boolean lattice Bn either admits a monochromatic copy of PP or a rainbow copy of QQ. We consider both weak and strong (non-induced and induced) versions of this problem.