The interplay of convex bodies and log-concave functions has attracted increasing attention in recent years and many notions in convex geometry have been extended to the set of log-concave functions. In this talk we will introduce some new connections between convex bodies and log-concave functions. This talk is based on the joint works with Prof. Jiazu Zhou.

In this talk, we first give a brief introduction to the optimal transport problem, and then its extension to nonlinear case with applications in geometric optics. Last, we introduce some recent results on the optimal partial transport problem, which is based on joint work with Shibing Chen (USTC) and Xu-Jia Wang (ANU).

We will discuss a class of Monge-Ampere type equations defined on the unit hypersphere, which are related to the Orlicz-Brunn-Minkowski theory in modern convex geometry. These equations are fully nonlinear partial differential equations, and could be degenerate or singular in different cases. We will talk about some recent results about the existence and non-uniqueness of solutions to these equations.

主要针对自由流体与多孔介质耦合问题数值方法中非线性问题、多物理问题耦合与多变量耦合系统等难点问题展开讨论：对于整个多物理耦合系统，我们主要采用高效解耦方法使得耦合问题求解化为各自物理域问题求解。进一步，针对耦合问题数值方法，我们分别有：1.对非线性问题针对稳态问题采取非奇异解束理论和非稳态问题采用small data假设来解决；2.对于Robin-Robin区域分解对稳态问题使用多物理迭代解耦方法，对非稳态问题采用多物理非迭代方法解耦方法；3.利用裂解算法求解复杂自由流Stokes问题，降低计算存储和规模，使得整个多变量耦合系统转化为拟椭圆问题或泊松问题求解、大规模的科学计算化为小规模计算。最后，我们针对现场油藏开采数值模拟进行简要汇报。

High order nonlinear weighted essentially non-oscillatory finite difference (WENO) schemes, which have the capability of capturing shocks essentially non-oscillatory while re-solving small scale structures efficiently, are popular for solving hyperbolic conservation laws. However, the WENO scheme is fairly complex to implement, computationally expen-sive and too dissipative for certain classes of problems. A natural way to alleviate some of these difficulties is to construct a hybrid scheme conjugating a nonlinear WENO scheme in the non-smooth stencils with a linear method in the smooth stencils. In this talk, I will briefly introduce the difficulties and recent development in the hybrid schemes.

报告人将介绍在高维唯一性问题领域的最新工作，包括三个方面：一是对于一般的可能线性退化的亚纯映射，在一个新类型的条件下得到的唯一性结果；二是分担 2n+2 个超平面的唯一性结果；三是分担较少超曲面的退化性和唯一性结果。

We define and study the harmonic heat flow for almost complex structures which are compatible with a Riemannian structure (M; g). This is a tensor-valued version of harmonic map heat flow. We prove that if the initial almost complex structure J has small energy(depending on the norm |/nabla J|), then the flow exists for all time and converges to a Kaehler structure. We also prove that there is a finite time singularity if the initial energy is sufficiently small but there is no Kaehler structure in the homotopy class. A main technical tool is a version of monotonicity formula, similar as in the theory of the harmonic map heat flow. We also construct an almost complex structure on a flat four tori with small energy such that the harmonic heat flow blows up at finite time with such an initial data.

题目：Numerical Method for the Maxwell Equations with Random Interfaces报告人：张凯 教授（吉林大学）地点：腾讯会议室时间：2020年6月9日 上午10:00-11:0