课题：国家重点研发项目“无穷维随机微分几何与 Malliavin 分析”理论

编号：2020YFA0712702

组织者：中国科学院数学与系统科学研究院 李向东

会议日程安排

线下和腾讯会议地址：

15日下午：南楼 N620     664-738-202

16日上午：南楼 N613     783-358-390

16日下午：南楼 N613     771-446-578

17日上午：南楼 N602     599-741-858

17日下午：南楼 N602     331-756-446

报告摘要

1、报告人：边伟 哈尔滨工业大学

报告题目：Anderson acceleration for nonsmooth fixed point problems

摘要：In this talk, we consider the convergence behavior of Anderson acceleration algorithm for nonsmooth fixed point problems. First, we prove convergence of Anderson acceleration for a class of nonsmooth fixed-point problems for which the nonlinearities can be split into a smooth contractive part and a nonsmooth part which has a small Lipschitz constant. Second, we propose a smoothing approximation of the composite max function and show that the smoothing approximation for a class of contractive mappings is also a contraction mapping and has the same fixed point as the original problem, which confirms that the nonsmoothness can not affect the convergence properties of Anderson(m) algorithm when we use the proposed smoothing approximation instead of the original nonsmooth one. Third, we propose a novel Smoothing Anderson(m) algorithm by using a smoothing function of the original fixed point function and show its r-linear convergence. Furthermore, we prove the q-linear convergence of the Smoothing Anderson(1) algorithm. Finally, some numerical examples are given to demonstrate the efficiency of the proposed smoothing Anderson acceleration algorithms.

2、报告人： 陈娴 厦门大学

报告题目：A variational formula for discrete-time Markov control processes under risk-sensitive average reward criterion

摘要：We study the risk-sensitive average reward criterion for discrete-time Markov control processes. The state space is a Borel space and the reward function can be unbounded. We prove the existence of a solution to the risk-sensitive average reward optimality equation and the existence of an optimal stationary policy via a new technique of constructing an  approximating sequence of coercive reward functions and introducing the split chain. Moreover,we develop a new approach to obtain a variational formula for the risk-sensitive average reward criterion without the compactness condition on the state space in the existing literature.

3、报告人：邓昌松 武汉大学

报告题目：Finite time blowup of solutions to fractional SPDEs

摘要: I shall talk about finite time blowup in the almost sure sense of a class of space-time fractional SPDEs. Both the cases of white noise and colored noise are considered. The sufficient and necessary condition between the blowup and Osgood condition is obtained when the spatial domain is bounded. The sufficient condition for the blowup is obtained when the spatial domain is the whole space.

4、告人：高洪俊 东南大学

报告题目：Averaging principle and large deviation for stochastic slow-fast systems driven by mixed noise
摘要： In this talk,I will talk about our recent results on averaging principle for stochastic slow-fast PDEs  and large deviation for stochastic slow-fast systems ODE driven by mixed noise under some conditions.

5、报告人：贾晨 北京计算科学研究中心

报告题目：复杂基因调控网络的随机过程与随机分析理论

摘要：基因调控是细胞内最重要的动力学过程，对细胞分化、细胞增殖、细胞凋亡、信号传导、压力响应，以及疾病的发生发展有着决定性的影响。基因调控网络的复杂性、随机性、非线性型与多尺度性给单细胞基因表达动力学的数学建模、理论分析与计算方法带来了极大的挑战。在本次汇报中，我将介绍团队在基因调控网络随机动力学方面的最新进展，包括严格数学理论、新型统计推断方法与高效高精度计算方法。

6、报告人：雷容 东北大学（Tohoku University)

报告题目：Homogenization of Stokes-Cahn-Hilliard equations with a logarithmic free energy for two-phase flow in porous media

摘要： In this talk,we investigate the homogenization of a phase-field model for two-phase,immiscible, and incompressible flow in porous media, incorporating surface tension effects. The model is governed by the coupled Stokes-Cahn-Hilliard system with a logarithmic free energy, where the two fluids are separated by a diffuse interface of finite width, assumed independent of the spatial scale parameter. By applying the method of two-scale convergence, we derive the homogenized limit, which takes the form of a generalized Richards’ equation that includes an additional correction term beyond the classical model. This is joint work with Prof. Jun Masamune.

7、报告人：刘党政 中国科学技术大学

报告题目：From mixing time of Markov chains to Tracy-Widom law of inhomogeneous random matrices

摘要：Consider symmetric and Hermitian random matrices whose entries are independent random variables with an arbitrary variance pattern. Under a novel Short-to-Long Mixing condition,which is sharp in the sense that it precludes a corrected shift at the spectral edge,we establish GOE/GUE edge universality for such inhomogeneous random matrices that may be sparse or far beyond the mean-field setting of classical random matrix theory. This condition effectively reduces the universality problem to verifying the mixing properties of Markov chains defined by the variance profile matrix. This talk is based on joint work with Guangyi Zou.

8、报告人：刘国平 华中科技大学

报告题目：On the Lagrange multiplier method to the Euler and Navier-Stokes equations on compact Riemannian manifolds

摘要：In this talk,we provide an explicit construction of a solution to the incompressible Euler and Navier-Stokes equations via the value function and Lagrange multiplier of a deterministic and stochastic optimal control problem on G=Diff(M),the group of diffeomorphisms. This talk is based on a joint work with Prof. Xiang-Dong Li.

9、报告人：刘伟 武汉大学

报告题目： Smoluchowski-Kramers approximation for stochastic differential equations

摘要：In this talk,we will show the Smoluchowski-Kramers approximation for McKean-Vlasov equations driven by fractional Brownian motion and Brownian motion respectively. The convergence rates for the total variation and L^p distance are obtained. In addition,we also study the large deviation,moderate deviation and central limit theorem. Furthermore,we will present our recent results about the Smoluchowski-Kramers approximation for invariant measures of SDEs/SPDEs by using stein's method.

10、报告人：马宇韬 北京师范大学

报告题目:Phase transition and convergence rate of spectral radius of product of complex Ginibre

摘要：

11、报告人：任艳霞 北京大学

报告题目：Moments of additive martingales of branching L\'evy processes and some applications

摘要：

12、报告人：王健 福建师范大学

报告题目：On the Spectra of a One-Dimensional Schr\"{o}dinger Operator with Random L\'evy Potentials

摘要：In this talk,we disscuss very preliminary results on the spectra of a one-dimensional Schr\"{o}dinger operator with general random L\'evy potentials.

Some questions are mentioned.

13、报告人：王宇钊 山西大学

报告题目：W-entropy formula for the Langevin deformation on the L^q-Wasserstein space over Riemannian manifolds

摘要：In this talk,inspired by the work of S.Li and X.-D.Li,we prove the W-entropy formula and rigidity theorem for the geodesic flow on the L^q-Wasserstein space over an n-dimensional complete Riemannian manifold with non-negative Ricci curvature,where q>1. We then introduce the Langevin deformation and prove the W-entropy-information formula and rigidity theorem for the Langevin deformation on complete Riemannian manifolds with non-negative Ricci curvature. The Langevin deformation can be regarded as an interpolation between the gradient flow of the Boltzmann entropy and the geodesic flow on the L^q-Wasserstein space. Our results improve a convexity result due to Lott based on the work by Lott and Villani. This is a joint work with Prof. X.-D. Li and Dr. R. Lei.

14、报告人：吴恋 中南大学

报告题目：Sharp matrix-weighted martingale inequalities

摘要：We introduce the martingale Ap condition for matrix weights and establish matrix-weighted Doob maximal inequalities for vector-valued martingales. The proof mainly relies on the idea of principal sets and new sparse dominations. Our approach enables us to obtain the optimal dependence of the constant on the characteristic of the weight involved. We also obtain quantitative weighted norm estimates for martingale square functions in both scalar-weighted and matrix-weighted settings.

15、报告人：张德飞 红河学院

报告题目：A G-stochastic epidemic model

摘要：In this talk,I will propose a new stochastic epidemic model driven by G-Brownian motion. The model embodies both the mean and variance uncertainty. It can be seen as an extension of the existing model. It shows a unique positive solution in the sense of quasi surely and will asymptotically tend to zero quasi surely and is pth-moment stable. (This talk based on joint work with Prof. Ping He and Prof. Yong Ren)

16、报告人：张土生 中国科学技术大学

报告题目：Exponential ergodicity of Stochastic Evolution Equations with reflection

摘要：In this paper,we establish an exponential ergodicity for stochastic evolution equations with reflection in an infinite dimensional ball. As an application,we obtain the exponential ergodicity of stochastic Navier-Stokes equations with reflection. A coupling method plays an important role.

17、报告人： 张旭 四川大学

报告题目：A convenient setting for infinite-dimensional analysis

摘要：In this lecture,I will present a convenient setting that we proposed for infinite-dimensional analysis,in which differentiation (in some weak sense) and integration operations can be easily performed,integration by parts can be conveniently established under rather weak conditions,and especially some nice properties and consequences obtained by convolution in Euclidean spaces can be extended to infinite-dimensional spaces in some sense by taking the limit. Compared to the existing tools in infinite-dimensional analysis,our setting enjoys more convenient and clearer links with that of finite dimensions,and hence it is more suitable for computation and studying some analysis problems in infinite dimensional spaces,particularly those in infinite-dimensional geometric analysis.