题目：Penetrating Sporadic Return Predictability报告人：涂云东 教授 （北京大学）地点：腾讯会议室时间：2022年10月13日 13:30-15:30摘要：Return predictability has been one of the central research questions in finance for many decades. This paper proposes a predictive regression with multiple structural changes to capture the sporadic predictive ability of potential predictors for the return series...

题目：Compressible Navier-Stokes Equations: Well-Posedness and Asymptotic Analysis报告人：何凌冰 教授 （清华大学）地点：腾讯会议室时间：2022年10月13日（星期四） 14：00-16：00摘要：In these three lectures, we will talk about recent progress on the well-posedness and asymptotic analysis for the compressible Navier-Stokes equations in the whole space. After a quick survey of the equations, we will...

题目：新冠早期四级响应和目前动态清零的数学模型及其风险评估报告人：林支桂 教授（扬州大学）地点：腾讯会议 ID 529 120 244 密码：123456时间：2022年9月13日（星期二）下午19：00—20：00摘要：本报告拓展经典的SEAIR和时滞IJR传染病模型, 研究新冠病毒防控的两种模式。首先以新的加权网络模型为主线, 以四级应急响应防控措施为核心, 重点引入离散的扩散算子和对流算子刻画城市内和城市间的传播, 研究在公共卫生应急分级响...

题目：Actor-Critic Reinforcement Learning in Continuous Time and Space报告人：贾颜玮 博士（哥伦比亚大学）地点：zoom线上会议 会议ID：86710704222， 密码：413890时间：2022年9月7日 21:30-22:30摘要：We study the actor-critic (AC) algorithms for reinforcement learning (RL) in continuous time and space under the regularized exploratory formulation developed by Wang et al. (2020). The first part of the...

Determining the behavior of viscous flows at small viscosity is one of the most fundamental problems in fluid mechanics. In this talk, we focus on the incompressible flow and study the vanishing viscosity limit of incompressible Navier-Stokes equations. It mainly involves the following contents:

An example of Apostolovet al. indicates that the condition of K-stability may not be correct one for general polarized manifolds. Szekelyhidi modified definition of K-stability by filtration and stated a variant of the Yau-Tian-Donaldson conjecture. We will talk about our proof of this variant of YTD conjecture for toric manifolds and homogeneous toric bundles. This is jointed with Li An-Min and Lian Zhao.

It has been a longstanding open problem to find a direct conservation law for harmonic mappings into manifolds. In the late 1980s, Chen and Shatah independently found a conservation law for weakly harmonic maps into spheres, which can be interpreted by Noether's theorem. This leads to Helein's celebrated regularity theorem on weakly harmonic maps from surfaces. For general target manifolds, Riviere discovered a direct conservation law in two dimension in 2007, allowing him to solve two well-known conjectures of Hildebrandt and Heinz. As observed by Riviere-Struwe in 2008, due to lack of Wente's lemma, Riviere's approach does not extend to higher dimensions. In a recent joint work with Chang-Lin Xiang, we successfully found a conservation law for a class of weakly harmonic maps into general closed manifolds in higher dimensions.

In this talk, we consider a family of character sums as multiplicative analogues of Kloosterman sums. We establish asymptotic formulae for any real (positive) moments of the above character sum as the character runs over all non-trivial multiplicative characters mod p, confirming a conjecture of Professor Wenpeng Zhang from 2002. Moreover, an arcsine law will be established as a consequence of the method of moments in probability theory. The arguments, amongst other tools, also allow us to obtain asymptotic formulae for moments of such character sums weighted by special L-values (at 1/2 and 1). The tools will include Gauss sums, hyper-Kloosterman sums, as well as a recent estimate for bilinear forms with general algebraic trace functions due to Fouvry, Kowalski and Michel.