In this talk, we will introduce the a priori method applied to the existence theory of elliptic PDEs in R^n and S^n. There are some open problems in this subject, especially for the degenerate elliptic PDEs. At last, we prove the existence theorem of the non-symmetric solutions of the homogeneous Lp dual Minkowski problem, which is a joint work with Yong Huang and Lu Xu

We study testing high-dimensional covariance matrices under a generalized elliptical model. The model accommodates several stylized facts of real data, including heteroskedasticity, heavy-tailedness, asymmetry, etc. We consider the high-dimensional setting where the dimension p and the sample size n grow to infinity proportionally, and establish a central limit theorem for the linear spectral statistic of the sample covariance matrix based on self-normalized observations. The central limit theorem is different from the existing ones for the linear spectral statistic of the usual sample covariance matrix.

题目：BSD Conjecture and ExplicitComputations of Jacobi Forms报告人：Prof. Nils-Peter Skoruppa （同济大学兼职教授德国锡根大学）时间：2018年4月3日 星期二10：30—11：30地点：致远楼101室欢迎各位师生参加

A class of staged-progression models with multiple age of infection structures and/or age of latency structures, are formulated to describe infectious disease progression with long latency and/or infectious period. Typical diseases include HIV and latent Tuberculosis. Global properties of these stage-age-structured models are fully analyzed using the Volterra-type Lyapunov functionals. I will also review recent progress and some research questions in these areas.

We present a systematically introduction to the Frozen Gaussian Approximation (FGA) for high-frequency seismic tomography in 3-D earth models. In the frozen Gaussian approximation (FGA) we approximate the seismic wavefield by a summation of frozen (fixed-width) Gaussian wave-packets propagating along ray paths. One can use a relatively small number of Gaussians to get accurate approximations of the high-frequency wavefield. Meanwhile, FGA algorithm can be perfectly parallelized, which speeds up the computation drastically with a high-performance computing station. In order to apply FGA to the computation of 3-D high-frequency seismic tomography, first we reformulate the FGA so that one can efficiently compute the Green's functions

$G(m,p,n)$ is an imprimitive complex reflection group for any positive integer $m,p,n$ with $p/mid m$. We introduce the reflection length $l_T$ and the reflection ordering $/preceq_{mp}$ on $G(m,p,n)$. We shall give some close formulae of $l_T(z)$ for any $z/in G(m,p,n)$ and some criteria for any $x,y/in G(m,p,n)$ to satisfy the relation $x/preceq_{mp}y$ when $(m,p)/in/{(1,1),(m,1),(m,m)/}$.

This study presents a new stochastic multiscale analysis approach to analyze the heat transfer performance of heterogeneous materials with random structures at different length scales. The heterogeneities of the materials are taken into account by periodic layouts of unit cells, consisting of randomly distributed inclusion dispersions and homogeneous matrix on the microscale and mesoscale. Based on the reiterated homogenization, a novel unified micro-meso-macro stochastic multiscale formulation is established and the scale gap is correlated by means of two-scale asymptotic expansions. Also, the stochastic multiscale formulae for computing the effective thermal property and temperature field are derived successively. Then, the stochastic prediction algorithm coupled with the finite element method is brought forward in details.

In this lecture, the speaker tries to present a proof of 2-dimensional Jacobian conjecture, based on several results established by the speaker mainly using the local bijectivity of Keller maps. The main contents in this lecture can be found in the paper recently posted to arxiv:1603.01867