We generalize the notions of ordinary points and singularities from linear ordinary differential equations to D-finite systems. Ordinary points and apparent singularities of a D-finite system are characterized in terms of its formal power series solutions. We also show that apparent singularities can be removed like in the univariate case by adding suitable additional solutions to the system at hand. Several algorithms are presented for removing and detecting apparent singularities. In addition, an algorithm is given for computing formal power series solutions of a D-finite system at apparent singularities. This is a joint work with Manuel Kauers, Ziming Li and Yi Zhang.

Log Fano manifold are generalization of Fano manifolds, and the canonical metrics on them are conic Kahler-Einstein metrics. I will talk about the existence of such metrics on log K-polystable log Fano manifolds.

We establish spreading properties of the Lotka-Volterra competition-diffusion system. When the initial data vanish on a right half-line, we show that there are two successive invasions. We derive the formulas of the exact spreading speeds and prove the convergence to homogeneous equilibrium states in between the invasion fronts. Our method is inspired by the geometric optics approach for Fisher-KPP equation due to the work of Freidlin, and that of Evans and Souganidis. Our main result settles an open question raised by Shigesada and Kawasaki in 1997, and shows that one of the species spreads to the right with a speed which is linearly, but non-locally, determined.

Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, regularized variations with large regularization parameter will degradate the performance in several important machine learning applications, and small regularization parameter will fail due to numerical stability issues with existing algorithms. We address this challenge by developing an Inexact Proximal point method for exact Optimal Transport problem (IPOT) with the proximal operator approximately evaluated at each iteration using projections to the probability simplex. The algorithm (a) converges to exact Wasserstein distance with theoretical guarantee and robust regularization parameter selection,

Let be an array of i.i.d. random variables, and let be a sequence of positive integers such that is bounded away from 0 and . The sample correlation matrix is generated from , , such that is the Pearson correlation coefficient between and . In this talk, we provide a supplement to Jiang's asymptotic distribution of the largest entry . We show that, for given nondecreasing function with ，there exists an array of symmetric i.i.d. random variables such that and, for some subsequence of , almost surely; does not exist almost surely; ， ，and does not convergence in distribution, where

We provide sufficient conditions on an initial curve for the area preserving and the length preserving curvature flows of curves in the plane, to develop a singularity at some finite time or converge to an m-fold circle as time goes to infinity. For the area preserving flow, the positivity of the enclosed algebraic area determines whether the curvature blows up in a finite time or not, while for the length preserving curvature flow, it is the positivity of an energy associated with initial curve that plays such a rule.

题目：从数学的角度看计算的本质与未来主讲人：姚鹏晖 副教授（南京大学 计算机科学与技术系）地 点：致远楼101室时 间：2019年5月17日15：30-16：30内容简介：理论计算机科学是计算机科学的一个分支，主要研究有关计算的逻辑化、抽象化和数学化的问题，从理论的角度回答 “什么是计算” 和 “怎样更高效地计算”这两个问题。这个报告中，将简要回顾下“计算”的历史，介绍当今计算机学家们对“计算”的理解，包括进入量子信息...

In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous across some smooth interface. Compared with the previous results for the inhomogeneous Navier-Stokes equations with constant viscosity, the main difficulty here lies in the fact that the L^1 in time Lipschitz estimate of the velocity field can not be obtained by energy method. Motivated by the key idea of Chemin to solve 2-D vortex patch of ideal fluid, namely, striated regularity can help to get the L^/infty boundedness of the double Riesz transform, we derive the a priori L^1 in time Lipschitz estimate of the velocity field under the assumption that the viscous coefficient is close enough to a positive constant in the bounded function space.