We study the positive solutions to a class of general semilinear elliptic equations ∆u(x) + uh(ln u) = 0 defined on a complete Riemannian manifold (M, g) with Ric(g) ≥ −Kg, and obtain the Li-Yau type gradient estimates of positive solutions to these equations which do not depend on the bounds of the solutions and the Laplacian of the distance function on (M, g). We also obtain some Liouville-type theorems for these equations when (M, g) is noncompact and Ric(g) ≥ 0 and establish some Harnack inequalities as consequences. Then, as applications of main theorem we extend our techniques to the Lichnerowicz-type equations

We develop a new class of distribution–free multiple testing rules for FDR control. I will mainly illustrate the idea via multiple testing with general dependence. A key element in our proposal is a symmetrized data aggregation (SDA) approach to incorporating the dependence structure via sample splitting, data screening and information pooling. The SDA substantially outperforms the knockoff method in power under moderate to strong dependence, and is more robust than existing methods based on asymptotic p-values. I will also talk about some other applications, such as the selection of the number of change-points and threshold selection in feature screening.

The theory of Gromov-Witten invariants is a curve counting theory defined by integration on the moduli of stable maps. Varying the stability condition gives alternative compactifications of the moduli space and defines similar invariants. One example is epsilon-stable quasimaps, defined for a large class of GIT quotients. When epsilon tends to infinity, one recovers Gromov-Witten invariants. When epsilon tends to zero, the invariants are closely related to the B-model in physics. The space of epsilon's has a wall-and-chamber structure. In this talk, I will explain how wall-crossing helps to compute the Gromov-Witten invariants and sketch a proof of the wall-crossing formula.

Combustion or ignition equation is a special reaction diffusion equation which is used to describe the propagation of flames. In this talk we consider the Cauchy problem and the Stefan free boundary problem for such equations. We will specify the asymptotic behavior for the solutions, in particular, the spreading phenomena and its feature in these problems.

题目：Variance Reduced Median-of-Means Estimator for Byzantine-Robust Distributed Inference报告人：刘卫东 教授（上海交通大学）地点：腾讯会议室时间：2021年10月13日（周三） 晚上19:30摘要：This talk develops an efficient distributed inference algorithm,  which is robust against a moderate fraction of Byzantine nodes, namely arbitrary and possibly adversarial machines in a distributed learning syst...

在这个数据科学越来越受到重视，数据越来越受到重视的今天，数据的科学治理与合规使用，也变得越来越重要。本次报告，围绕以下几个方面：第一、目前我们看到的数据合规案例和问题有哪些。第二、目前我国同数据合规使用相关的法律条文有哪些。第三、在过去的这些年里，同数据相关的司法诉讼经典案例，做有挑选的探讨。最后，对我国数据合规使用有指导性的基本原则做了总结。

I will present some recent work on the heat equation and the biharmonic heat equation on complete Riemannian manifolds, including: uniqueness criteria for the heat equation and the biharmonic heat equation, estimates of the biharmonic heat kernel, and a uniform L-infinite estimate for solutions of the biharmonic heat equation with bounded initial data.

We develop a dynamic tractable model where an investor derives realization utility as in Barberis and Xiong (2012) and Ingersoll and Jin (2013), but importantly can dynamically rebalance her portfolio between a risky asset and a risk-free asset. We show that the option of investing in the risk-free asset is quite valuable, even though the investor only derives utility from realized gains and losses of trading the risky asset. We also find that the investor may realize losses after a slight rally following a crash. This work is jointly with Cong Qin and Neng Wang