The theme of this lecture centers around two famous books, one by Hermann Weyl on “The Classical Groups: Their Invariants and Representations” (1939), another the six-volume work by I.M. Gelfand et al. on “Generalized Functions” (1960’s). I will discuss some broad ideas related to the theme of these two books, as well as some recent development in classical groups and their smooth representations. The talk is aimed at a general

基于对丛代数的Poisson结构与其量子化的关系的研究，我们通过对量子丛代数的Poisson结构的刻画，提出了二次量化的概念，并对不含系数的量子丛代数，给出了它的二次量子化的形态，指出了在这个情形下，其二次量子化具有相对的平凡性。

In this talk, we consider the global existence of Yamabe flow and study the global behavior of the Yamabe flow in a complete noncompact Riemannian manifold. We also use the variational method to study the existence problem of metrics with constant scalar curvature on complete noncompact Riemannian manifolds and we can give a partial affirmative answer to a question posed by J.Kazdan in 1982.

I will talk about the construction of irreducible holonomic modules over quantum coordinate algebra. This is a joint work with Ruibin Zhang.

在这个报告中，将从风险的实际情况、经典的风险模型提出，考虑因素的完善、模型的演变过程出发，探讨计数时间序列的应用及推断。

In this talk, I will introduce our recent work on low-rank methods for Bayesian inverse problems. For linear problems with Gaussian noise and Gaussian prior, the posterior is also Gaussian and characterized by the posterior mean and covariance. We propose a low-rank Arnoldi method to approximate the large dense posterior covariance matrix by making use of tensor computations. For nonlinear systems, the posterior is not Gaussian anymore, however, can often be approximated by a Gaussian distribution using the ensemble Kalman filter (EnKF) or the extended Kalman filter (ExKF).

When estimating the average causal effect in observational studies, researchers have to tackle both self-selection of treatment and outcome modeling. This is difficult since usually there are a large number of covariates that affect people's treatment decision and the true functional form in the model is not known. Propensity score is a popular approach for dimension reduction in causal inference. We propose a new semiparametric estimation strategy using B-spline based on the propensity score, which does not rely on parametric model specification. We further improve the efficiency of the estimator by addressing the error heteroscedasticity. We also establish the asymptotic properties of both estimators.

In this talk, we will first review the existing results and methods on the exact controllability for the 1-D coupled hyperbolic system by means of boundary controls on one side. Then, we will show our recent results on this topic on how the sufficient and necessary boundary coupling effect on the non-control side can be used to shorten the control time as much as possible no matter how the coupling terms appearing in the equations. In particular, this is done under natural conditions on the regularity of the coefficients and arbitrary number of coupled transport PDEs in either direction. Several counterexamples and interesting phenomena will also be shown.