Title: 斜积流的Sarnak猜想
Speaker: 刘建亚（山东大学）
Datetime: 2020-06-04 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：965 0633 0103
Password：545872
Abstract
Sarnak猜想预测，Mobius函数与零熵的动力系统正交。本演讲将介绍这个猜想在非正则斜积流情形的一些进展。
Title: The vanishing discount problem for the system of HJ equations: the full convergence and a counterexample
Speaker: 严军（复旦大学）
Datetime: 2020-06-09 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：971 6180 7575
Password：010142
Abstract
证明耗散型接触Hamilton动力系统全局吸引子的存在性，并给出所在区域的一个细致刻画。
Title: Viscosity solution of HJ equation: existence, structure of solution set and large time behavior
Speaker: 王林（清华大学）
Datetime: 2020-06-11 15:00 — 16:00 Beijing/Shanghai
Venue: 腾讯会议 APP
Meeting ID：218 308 213
Password：654321
Abstract
I will talk about some new results on the topics listed in the title. It is based on some works joint with X. Shu, K. Wang and J. Yan.
Title: The vanishing discount problem for the system of HJ equations: the full convergence and a counterexample
Speaker: Hitoshi Ishii（Tsuda University & Waseda University）
Datetime: 2020-06-18 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：963 4455 9881
Password：372924
Abstract
I discuss the vanishing discount problem for the system of HJ equations with the focus on the full convergence of the solutions of the discounted problems as the discount factor tends to zero. I recall joint work with Liang Jin which has established the full convergence result under the convexity, coercivity, and monotonicity hypotheses, and I explain an example of the "non-convex" system, for which the whole family of the solutions of the discounted problems does not converge.
Title: The Lax-Oleinik representation in non-compact setting
Speaker: Albert Fathi（Georgia Tech）
Datetime: 2020-06-18 21:00 — 22:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：993 2636 1438
Password：144541
Abstract
We will be interested in viscosity solutions of the evolution Hamilton-Jacobi equation
\[
\partial _tU+H(x,\partial_xU)=0.
\]
Here we think of the case where \(U:[0,+\infty[\times M\to\mathbb{R}\), with \(M\) is a manifold.
If \(M\) is compact, as has been known for a long time, the maximum principle yields uniqueness for a given initial condition \(U\vert_{\{0\}\times M}\). This in turn implies the representation by a Lax-Oleinik type formula. When \(M\) is not compact, the global maximum principle does not immediately hold. Hitoshi Ishii and his coworkers obtained results about 10 years ago under some restrictions when \(M=\mathbb{R}^n\). Basically the restrictions are about controlled growth at infinity.
We will explain that under the hypothesis that H is Tonelli, all continuous solutions of the evolution Hamilton-Jacobi equation above satisfy the Lax-Oleinik representation even for non-compact \(M\). This of course will imply uniqueness for a given initial condition. Moreover, we will also show that if any pointwise finite \(U\) is given by the Lax-Oleinik representation is automatically continuous and therefore a viscosity solution.
Title: First Order Mean Field Games--existence and long-time behavior of solutions
Speaker: 王楷植（上海交通大学）
Datetime: 2020-06-25 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：688 9993 3634
Password：394033
Abstract
First I will give a short introduction of the theory of mean field games, which was introduced independently by Lasry and Lions, and Huang, Malhame and Caines to study Nash equilibria for games with a very large number of players. And then I will introduce two long-time behavior results of solutions to evolutionary MFGs system on Rd [P. Cannarsa, W. Cheng, C. Mendico, K. Wang, Dyn. Games Appl., 2020] and with state constraints [P. Cannarsa, W. Cheng, C. Mendico, K. Wang, arXiv: 2004.06505], respectively. At last, I will talk about some new existence results of solutions of discounted stationary MFGs system and of more general (than discounted one) system.
Title: 复动力系统介绍
Speaker: 王跃飞 （中科院数学所）
Datetime: 2020-07-01 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：641 6124 6859
Password：381409
Title: Interface Profile Near the Contact Line in Electro-Wetting on Dielectric
Speaker: Weiqing REN（任维清）（National University of Singapore）
Datetime: 2020-07-02 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：688 9993 3634
Password：394033
Abstract
We consider a charged droplet sitting on a dielectric substrate and study the static profile of the interface near the contact line. We first derive the governing equations using the principle of minimum energy, then discuss the distinguished limit of the model. Analysis of the inner problem, which governs the interface profile near the contact line, shows the existence of a well-defined apparent contact angle. The apparent contact angle depends on the applied voltage and the thickness of the dielectric substrate, and the relation agrees well with the empirical Young-Lippmann equation.
Title: On the relations between principal eigenvalue and torsional rigidity
Speaker: Giuseppe Buttazzo（Università di Pisa）
Datetime: 2020-07-15 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：647 9139 0694
Password：548896
Abstract
The relations between principal eigenvalue of the Laplace operator and torsional rigidity are studied in the class of general domains, convex domains, and domains with a small thickness. This is of help to provide some bounds for the Blasche-Santaló diagram of the two quantities. The results have been obtained in a joint work with Michiel van den Berg (Bristol) and Aldo Pratelli (Pisa).
Title: Weak KAM and Aubry–Mather theory On graphs
Speaker: Antonio Siconolfi（Università degli Studi di Roma “La Sapienza” ）
Datetime: 2020-07-21 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：654 5189 5068
Password：757748
Abstract
Even if the structure of graphs is very simple, we show that it is possible to build an adaptation of Weak KAM and Aubry Mather theory in this setting, for a suitable class of Hamiltonians. We recover the main properties of the continuous case. One of the applications we have in mind, , still under investigation, is to extend the homogenization result for Hamilton–Jacobi equations on graphs/networks. A further possible application is to define and study a first order time–dependent Mean Field Games system in this setting. Work in collaboration with Alfonso Sorrentino.
Title: Weak solutions of second order master equations for mean field games with common noise
Speaker: Chenchen MOU（牟宸晨）（UCLA & City University of Hong Kong）
Datetime: 2020-07-27 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：621 0545 9046
Password：224299
Abstract
In this talk we study master equations arising from mean field game problems, under the crucial monotonicity conditions. Classical solutions of such equations require very strong technical conditions. Moreover, unlike the master equations arising from mean field control problems, the mean field game master equations are non-local and even classical solutions typically do not satisfy the comparison principle, so the standard viscosity solution approach seems infeasible. We shall propose a notion of weak solution for such equations and establish its wellposedness. Our approach relies on a new smooth mollifier for functions of measures, which unfortunately does not keep the monotonicity property, and the stability result of master equations. The talk is based on a joint work with Jianfeng Zhang.
Title: Equilibrium states which is not Gibbs measure on hereditary subshifts
Speaker: 陈二才（南京师范大学）
Datetime: 2020-08-26 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：618 1982 4695
Password：568810
Abstract
We consider consider which kind of invariant measure on hereditary subshifts is not Gibbs measure. For the hereditary closure of a subshift \((X,S)\), we prove that in some situation, the invariant measure \(\nu\ast B_{p,1-p}\) can not be Gibbs measure where \(\nu\) is any invariant measure on \((X,S)\). As an application, we show that for some \(\mathscr{B}\)-free shifts, the equilibrium state \(\nu_{\eta}\ast B_{p,1-p}\) is not Gibbs measure.
Title: Multiplicity of closed geodesics on Finsler compact non-simply connected manifolds
Speaker: 刘会（武汉大学）
Datetime: 2020-09-02 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：672 9144 4139
Password：130178
Abstract
For many years, there seem to be very few works on the multiplicity of closed geodesics on non-simply connected manifolds, the main reason is that the topological structures of the free loop spaces on these manifolds are not well known, so that the classical Morse theory is difficult to be applicable. In recent years, motivated by the studies on simply connected manifolds and closed characteristics on Hamiltonian energy surfaces, we study the topological structure of the contractible component and non-contractible component of the free loop space on Finsler real projective space and compact space form, which are typically non-simply connected manifolds, and then we establish some new resonance identities, which are successfully applied to get many multiplicity results of closed geodesics on these non-simply connected manifolds. In this talk, I will give a survey of our results.
Title: Restricted independence in displacement function
Speaker: 张伟年（四川大学）
Datetime: 2020-09-09 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：651 2716 6946
Password：562374
Abstract
Since the independence of focal values is a sufficient condition to give a number of limit cycles arising from a center-focus equilibrium, in this paper we consider a restricted independence to a parametric curve, which gives a method not only to increase the lower bound for the cyclicity of the center-focus equilibrium but also to be available when those focal values are not independent. We apply the method to a nondegenerate center-focus system and prove that the cyclicity reaches its an upper bound. This is a joint work with Xingwu Chen, Jaume Llibre, Zhaoxia Wang.
Title: 动力系统中的光滑不变流形和不变叶层问题
Speaker: 张文萌（重庆师范大学）
Datetime: 2020-09-09 16:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：651 2716 6946
Password：562374
Abstract
不变流形和不变叶层是微分动力系统中的核心研究对象。相关结论在正规形，分岔，遍历性等问题中都有关键应用。这次报告中我们将讨论当经典的图像变换法与Lyapunov-Perron方法无法使用时，如何在无谱间隙条件或无谱约束条件下找到光滑不变流形和不变叶层。
Title: On the existence of SRB measures for a class of partially hyperbolic attractors
Speaker: 曹永罗（苏州大学）
Datetime: 2020-09-23 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：652 9681 7446
Password：934366
Abstract
In this talk, we consider the existence of SRB measure for partially hyperbolic attractors. If the systems's central direction can be decomposed into one dimension sub-bundles which are dominated splitting, then there exists a SRB measure.
Title: Pseudo solutions, rotation sets, and shadowing rotations for monotone recurrence relations
Speaker: 秦文新（苏州大学）
Datetime: 2020-09-23 16:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：652 9681 7446
Password：934366
Abstract
By introducing for monotone recurrence relations pseudo solutions, which are analogues of pseudo orbits of dynamical systems, we show that for general monotone recurrence relations the rotation set is closed, and each element in the rotation set is realized by a Birkhoff orbit. Moreover, if there is an orbit without rotation number, then the system has positive topological entropy, and we can construct orbits shadowing different rotation numbers.
Title: Regularity and generic divergence of local first integrals for analytic systems
Speaker: 张祥（上海交通大学）
Datetime: 2020-09-28 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：676 5125 5799
Password：955117
Abstract
In this talk we first introduce background on local integrability of analytic differential systems, and then present our recent results about regularity and generic divergence of analytic differential systems near a singularity with one zero eigenvalue and others nonresonant. These results answer the related problems partially existing from 2003.
Title: Denjoy subsystems and Horseshoes
Speaker: Marie-Claude Arnaud（Université Paris Diderot）
Datetime: 2020-10-08 14:30 — 15:30 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：685 3634 5303
Password：394960
Abstract
I will describe some connections between two kinds of restricted dynamics for area preserving diffeomorphisms, horseshoes and Denjoy subsystems: this last notion has been introduced by myself and P. Le Calvez and I will explain it. Then I will explain that any horseshoe contains a continuous 1-parameter family of Denjoy subsystems that is parametrized by the rotation number. After that, I will consider the inverse problem and give some partial answer: if an area preserving diffeomorphism \(f\) has a Denjoy subsystem, does there exist a horseshoe for \(f\)?
Title: Hamilton-Jacobi方程解的长期行为：从动力系统的观点看
Speaker: 严军（复旦大学）
Datetime: 2020-10-13 15:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：637 8719 4462
Password：432472
Abstract
从动力系统的角度，研究Hamilton-Jacobi方程解半群全局吸引子的存在性，吸引子的特征指数，以及不动点之间的连接轨道的存在性。
Title: Rigorous theory of viscous and inviscid 1d turbulence
Speaker: Sergei Kuksin（Université Paris Diderot）
Datetime: 2020-10-21 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：687 5772 3983
Password：500347
Abstract
I will present three main laws from the Kolmogorov theory of turbulence ("the K41 model"), discuss their versions for one-dimensional fluid and will show that the latter may be rigorously justified for the 1d fluid, described by the Burgers equation with small positive or zero viscosity. The proof relies on a qualitative analysis of the dynamical system which the Burgers equation with small positive viscosity defines in Sobolev spaces. The talk is based on my joint book with Alex Boritchev which will appear next year in Publications of AMS.
Title: Lyapunov optimizing measures and periodic measures for \(C^2\) expanding maps
Speaker: 黄文（中国科学技术大学）
Datetime: 2020-10-27 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：693 5063 1465
Password：188759
Abstract
We consider the typical Lyapunov minimizing measures for expanding self-maps on the circle. The main result obtained in this paper is that there exists an open and dense subset \(\mathscr{P}\) of all \(C^2\) expanding self-maps such that for each \(T\in\mathscr{P}\), the Lyapunov minimizing measures of \(T\) are uniquely supported on a periodic orbit. This answers a conjecture of Jenkinson-Morris positively. This is a joint work with Leiye Xu and Dawei Yang.
Title: Characteristic Factors in Dynamical Systems
Speaker: 邵松（中国科学技术大学）
Datetime: 2020-10-27 16:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：693 5063 1465
Password：188759
Abstract
In this talk, we will discuss characteristic factors in dynamical systems. First we give some examples to show what are characteristic factors. Then we show some recent results about characteristic factors in dynamical systems and their applications. This is a joint work with Wen Huang, Xiangdong Ye etc.
Title: Ergodic Optimization of a sequence of continuous obervables
Speaker: 赵云（苏州大学）
Datetime: 2020-10-28 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：676 0808 8080
Password：969567
Abstract
In this talk, we will review some research progresses in ergodic optimization for a single continuous function, and give some results of the ergodic optimization for a sequence of continuous functions, including subordination principle, constrained ergodic optimization and typical properties.
Title: Frenkel-Kontorova模型中的有序结构
Speaker: 王亚南（南京师范大学）
Datetime: 2020-10-28 16:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：676 0808 8080
Password：969567
Abstract
Frenkel-Kontorova模型（F-K模型）描述了一列相互作用的粒子在给定势能下的运动规律。系统的有序结构对于系统的稳定性有重要意义。在本报告中，我们主要讨论过阻尼的F-K模型中有序结构性质，主要包括叶状结构存在的判定，层状结构性质及其性质。
Title: Small amplitude generalized breathers for nonlinear Klein-Gordon equations
Speaker: Chongchun Zeng（Georgia Institute of Technology）
Datetime: 2020-10-30 10:00 — 11:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：613 9977 2969
Password：914914
Abstract
Breathers are temporally periodic and spatially localized solutions of evolutionary PDEs. They are known to exist for integrable PDEs such as the sine-Gordon equation, but are believed to be rare for general nonlinear PDEs. When the spatial dimension is equal to one, exchanging the roles of time and space variables (in the so-called spatial dynamics framework), breathers can be interpreted as homoclinic solutions to steady solutions and thus arising from the intersections of the stable and unstable manifolds of the steady states.
In this talk, we shall study small breathers of the nonlinear Klein-Gordon equation generated in an unfolding bifurcation as a pair of eigenvalues collide at the original when a parameter (temporal frequency) varies. Due to the presence of the oscillatory modes, generally the finite dimensional stable and unstable manifolds do not intersect in the infinite dimensional phase space, but with an exponentially small splitting (relative to the amplitude of the breather) in this singular perturbation problem of multiple time scales. This splitting leads to the transversal intersection of the center-stable and center-unstable manifolds which produces small amplitude generalized breathers with exponentially small tails. Due to the exponential small splitting, classical perturbative techniques cannot be applied. We will explain how to obtain an asymptotic formula for the distance between the stable and unstable manifold of the steady solutions. This is a joint work with O. Gomide, M. Guardia, and T. Seara.
Title: On a Hamiltonian approach towards hydrodynamic limit for non-interacting deterministic particles
Speaker: Jin FENG（University of Kansas）
Datetime: 2020-11-04 20:00 — 21:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：624 1270 2131
Password：449409
Abstract
In the context of hydrodynamic limit for \(N\) non-interacting particles following Hamiltonian dynamics, we identify a type of scaling where we can avoid explicit use of micro-canonical, canonical ensembles and even arguments about equivalence/non-equivalence of ensembles. Replacing them is a deterministic averaging problem studied in the finite dimensional weak KAM theory. As a consequence, we derive a continuum level effective-Hamiltonian as limit from the particle Hamiltonians.
We formulate the above program using well-posedness and multi-scale convergence of first order Hamilton-Jacobi PDEs in the space of probability measures, in a viscosity sense. An extended half-relaxed limit theory and a comparison principle for the Hamilton-Jacobi can be developed exploring two inter-related abstract aspects of the Wasserstein space: One, it is a limit of quotient space of \(N\)-products of Euclidean spaces modeling individual particles; Two, it is an Alexandrov metric spaces with curvature bounded from below.
This is work in progress with Toshio Mikami in Tsuda University, Japan.
Title: Weak KAM Theory for Sub-Riemannian control systems
Speaker: Cristian Mendico（GSSI-Gran Sasso Science Institute）
Datetime: 2020-11-05 16:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：665 8976 3941
Password：044735
Abstract
The ergodic behavior of control systems is an open and challenging problem since such a systems give rise to non-coercive and not strictly convex Hamiltonian even if the original Lagrangian is of Tonelli type. I will analyze the class of Sub-Riemannian control systems, i.e. system of the form \[\dot\gamma(t)=\sum_{i=1}^{m}{f_{i}(\gamma(t))u_{i}(t)}\] for a given set of vector fields \(\{f_{i}\}_{i = 1, \dots m}\). The assumptions on the model that will play a crucial role are the Chow's condition and the non-existence of singular control for the convergence result and for the Aubry-Mather theory, respectively.
For a Lagrangian \(L\) and a time horizon \(T>0\) we, first, obtain that time-average value function converge to a real constant \(c(L)\) as \(T \to +\infty\). Then, we show the ergodic Hamilton-Jacobi equation \[H(x, Du(x))=c(L), \quad x \in \mathbb{R}^{d}\] has a continuous viscosity solution and moreover, we provide a representation formula for such a constant, in the spirit of Mather's results, by using closed measures.
In conclusion we define the (projected) Mather set and the Aubry set associated with this systems and we study the regularity of a solution to the ergodic equation on these sets.
Title: KAM theory and quasi-periodic attractors for conformally symplectic systems
Speaker: Alessandra Celletti（University of Rome Tor Vergata）
Datetime: 2020-11-13 16:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：686 3847 7527
Password：947724
Abstract
We present results on the existence of quasi-periodic attractors of conformally symplectic systems in non-perturbative regimes. Conformally symplectic systems are characterized by the property that they transform the symplectic form into a multiple of itself. Finding the solution of such systems requires to add a drift parameter. We provide an explicit quantitative theorem in an a-posteriori format. Precisely, assuming the existence of an approximate solution, satisfying the invariance equation up to an error term - small enough with respect to explicit condition numbers, - then we can prove the existence of a solution nearby.
This method can be also used to get different results: (i) prove the existence of whiskered tori for conformally symplectic systems, (ii) give a characterization of the analyticity domains of the quasi-periodic attractors in the symplectic limit, (iii) provide a very efficient algorithm to generate the solution, which can be implemented successfully in model problems and physically meaningful examples.
The content of this talk refers to works in collaboration with R. Calleja and R. de la Llave.
Title: On the vanishing discount problem from the negative direction
Speaker: Andrea Davini（University of Rome La Sapienza）
Datetime: 2020-11-17 16:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：650 6594 4606
Password：472578
Abstract
It has been proved in A. Davini, A. Fathi, R. Iturriaga and M. Zavidovique, Invent. Math. (2016) that the unique viscosity solution of
\begin{equation}\label{abs}\tag{*}
\lambda u_\lambda+H(x,d_x u_\lambda)=c(H)\qquad\hbox{in \(M\)},
\end{equation}
uniformly converges, for \(\lambda\rightarrow 0^+\), to a specific solution \(u_0\) of the critical equation
\[
H(x,d_x u)=c(H)\qquad\hbox{in $M$},
\]
where \(M\) is a closed and connected Riemannian manifold and \(c(H)\) is the critical value.
In this seminar, we will consider the same problem for \(\lambda\rightarrow 0^-\). In this case, viscosity solutions of equation \eqref{abs} are not unique, in general, so we focus on the asymptotics of the minimal solution \(u_\lambda^-\) of \eqref{abs}. Under the assumption that constant functions are subsolutions of the critical equation, we prove that the \(u_\lambda^-\) also converges to \(u_0\) as \(\lambda\rightarrow 0^-\). Furthermore, we exhibit an example of \(H\) for which equation \eqref{abs} admits a unique solution for \(\lambda<0\) as well. The talk is based on a joint work with Lin Wang (Tsinghua University).
Title: Euclidean distance function in the presence of an obstacle
Speaker: Piermarco Cannarsa（University of Rome Tor Vergata）
Datetime: 2020-11-19 16:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：680 9256 2983
Password：472595
Abstract
The obstacle problem is a classical topic in analysis, which may take different forms depending on the quantities you observe. In this talk, we are interested in the regularity of the Euclidean distance function from a given point in the presence of a compact obstacle with smooth boundary. First, we will show that the distance is semiconcave with a fractional modulus and that, near the obstacle, such a regularity is optimal. Then, we will show that the distance function is everywhere differentiable (except for the point target) if and only if no obstacle is present. Finally, we will study the propagating structure of the singular set of the distance both at `interior points' and on the boundary of the obstacle. For such an analysis, we will use recent results on the extension of semiconcave functions defined on a closed domain. This is joint work with Paolo Albano and Vincenzo Basco.
Title: Generic Behavior of smooth monotone systems with respect to \(k\)-cones
Speaker: 王毅（中国科学技术大学）
Datetime: 2020-11-24 14:00 — 15:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：640 5432 5516
Password：960028
Abstract
In this talk, we consider a smooth flow which is ”strongly monotone“ with respect to a \(k\)-cone, a closed set that contains a linear subspace of dimension \(k\) and no linear subspaces of higher dimension. We will show that orbits with initial data from an open and dense subset of the phase space are either pseudo-ordered or convergent to equilibria. This covers the celebrated Hirsch's Generic Convergence Theorem in the case \(k=1\), and yields a generic Poincaré-Bendixson Theorem for the case \(k=2\).
Title: Spreading speeds of nonlocal diffusion KPP equations
Speaker: 梁兴（中国科学技术大学）
Datetime: 2020-11-24 15:00 — 16:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：640 5432 5516
Password：960028
Abstract
In this talk I will introduce our work on the dynamics of KPP nonlocal diffusion equation on one-dimensional space. We will discuss the relation between the the existence of the spreading speed and the irreducibility of the diffusion kernel.
Title: The limit distribution of inhomogeneous Markov processes and Kolmogorov's problem
Speaker: 柳振鑫（大连理工大学）
Datetime: 2020-11-27 14:00 — 15:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：643 9526 4495
Password：956128
Abstract
In this talk, we will talk about the limit distribution of inhomogeneous Markov processes generated by SDEs. Meantime, we will also discuss the recent progress in Kolmogorov's problem on the limit behavior of stationary distributions of diffusion processes as the diffusion tends to zero.
Title: From homogenization to dynamical system
Speaker: Yifeng Yu（University of California, Irvine）
Datetime:
Venue: Zoom APP
Meeting ID：632 3890 1470
Password：365272
Abstract
In these three talks, I will (1) go over the basic theory of homogenization of Hamilton-Jacobi equations; and (2) talk about how to use Aubry-Mather theory to solve some fundamental problems in homogenization theory that can not be approached by standard PDE tools.
This mini-course is composed of three parts:
Title: On the regularity of length-minimizers in sub-Riemannian geometry
Speaker: Davide Barilari（Università degli Studi di Padova）
Datetime: 2020-12-04 19:00 — 20:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：632 8456 8140
Password：902547
Abstract
The regularity issue for length-minimizers is one of the main open problem in sub-Riemannian geometry. In this talk, after presenting the question and giving a survey of the known results, we present a recent result on the \(C^1\) regularity for a class of length-minimizers in rank 2 sub-Riemannian structures. (Joint with Yacine Chitour, Frédéric Jean, Dario Prandi, Mario Sigalotti)
Title: Noise Impacts on Finite Dimensional Dynamical Systems
Speaker: Yingfei Yi（University of Alberta and Jilin University）
Datetime: 2020-12-08 14:00 — 15:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：627 0593 7107
Password：811969
Abstract
Dynamical systems are often subjected to noise perturbations either from external sources or from their own intrinsic uncertainties. While it is well believed that noises can have dramatic effects on the stability of a deterministic system at both local and global levels, mechanisms behind noise surviving or robust dynamics have not been well understood especially from distribution perspectives. This talk attempts to outline a mathematical theory for making a fundamental understanding of these mechanisms in white noise perturbed systems of ordinary differential equations, based on the study of stationary measures of the corresponding Fokker-Planck equations. New existence and non-existence results of stationary measures will be presented by relaxing the notion of Lyapunov functions. Limiting behaviors of stationary measures as noises vanish will be discussed in connection to important issues such as stochastic stability and bifurcations.
Title: Smooth Conjugacy for Random Dynamical Systems
Speaker: kening Lu（Brigham Young University）
Datetime: 2020-12-11 09:30 — 11:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：641 3668 9354
Password：671320
Abstract
In this talk, we study the smooth conjugacy problems for random dynamical systems when the Lyapunov exponents satisfy various conditions such as Diophantine conditions, nonresonant conditions.
Title: The Banach-Tarski Paradox
Speaker: 郭坤宇（复旦大学）
Datetime: 2020-12-16 16:00 — 17:00 Beijing/Shanghai
Venue: Zoom APP
Meeting ID：693 9528 7788
Password：924002
Abstract
Banach-Tarski “悖论” 说： 三维空间中的任何一个球，可分解成有限“块”， 其中一些“块”经过平移和旋转拼成和原球同样大小的球， 剩下的一些“块”也能经过平移和旋转拼成和原球同样大小的球。这是数学中最惊奇的结论之一， 也是集论几何研究的出发点。 本讲座主要介绍 Banach-Tarski “悖论”与测度论、泛函分析、群论以及数学中的选择公理之间的深刻联系。