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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

Although there are many known K/"ahler-Einstein manifolds, there is so far no very practical method to check a given compact Fano manifold to be K/"ahler-Einstein or not.This is also true for the K/"ahler metrics with constant scalar curvatures or Calabi extremal metrics. The situation for a cohomogeneity one metrics was completely resolved.For the type III case, it was solved in my dissertation in 1992. For the remain type I and II case, the existence is equivalent to the negativity of a topological integral.The type I case was published in 2011. Therefore, the problem is reduced to check the negativity for classes of Fano manifolds. Recently, we use computer to get some insight into a few classes of type I Fano manifolds. This work is a joint work with a group of students.

The study of constant scalar curvature Kahler metrics with cone singularities is motivated from the Yau-Tian-Donaldson conjecture. We would present the recent progress in the constant scalar curvature Kahler metrics with cone singularities, including regularity, existence and uniqueness. We would also discuss the application to the constant scalar curvature Kahler metric problem.