动力系统是一个与微分方程，群论，数论，几何，拓扑等领域紧密联系深入交叉的数学的研究领域。 近年来，动力系统领域蓬勃发展，出现了很多新的思想方法。为发展国内动力系统，推进动力系统学科的教育，促进国内外学生与专家学者的交流。特举办2026年动力系统暑期讲习班。
课程信息
课程日期: 2026年6月29日--7月10日(29日报到，10日离会)
举办地点: 清华大学（线下）
招生人数: 80人(校外)
授课老师:
Aaron Brown(美国西北大学）
何伟鲲(中国科学院数学与系统科学研究院)
Egor Shelukhin(蒙特利尔大学)
孙文博(弗吉尼亚理工大学)
杨磊(新加坡国立大学)
课程设置
报告一：
主讲人：Aaron Brown(美国西北大学)
Title: Random dynamics, stationary measure, and rigidity
Abstract: Stationary measures are natural objects to study in the settings of iterated functions systems, actions of finitely generated (non-amenable) groups, and i.i.d. random dynamical systems.
I will present (1) background and motivation in dynamical systems and examples of fractal invariant and stationary measures in dynamical systems, (2) outline many recent results classifying stationary measures in the setting of homogeneous dynamical systems, and (3) discuss some of my joint projects aimed at establishing analogous results in the setting of non-linear and dissipative random dynamics.
报告二：
主讲人：何伟鲲(中国科学院数学与系统科学研究院)
Title: Quantitative equidistribution of random walks on homogeneous spaces
Abstract: Consider the action of a Lie group on a homogenous space, that is, the quotient space by a lattice subgroup. The dynamics of such action has many rigidities. The most prominent example are the Ratner theorems on unipotent flows. As an analogue to flows, we may consider random walks on such spaces. Benoist-Quint proved the analoguous rigidity theorems around 2010s. It is until recently we saw the beginning of making Benoist-Quint's rigidity theory quantitative and effective. In this short course, I will present important ideas of these developments in a simpler setting of a random walk on a torus. This includes an introduction to random matrix products, spectral gaps and projection theorems . New materials are based on joint works with Timothée Bénard.
报告三：
主讲人：Egor Shelukhin(蒙特利尔大学)
内容：待定
报告四：
主讲人：孙文博(弗吉尼亚理工大学)
Title:Spherical higher order Fourier analysis
Abstract: Classical Fourier analysis provides a powerful framework for studying linear patterns in functions and sets, with deep applications across number theory, combinatorics, ergodic theory, and theoretical computer science. However, many problems involving polynomial configurations and higher-degree correlations lie beyond the reach of classical methods. Higher-order Fourier analysis was developed to address this limitation.
This summer school will introduce the main ideas and tools of higher-order Fourier analysis, with a focus on its recent development in the spherical setting and applications in the Geometric Ramsey Conjecture. Topics may include Gowers uniformity norms, inverse theorems, nilsequences and nilmanifolds, polynomial phases, decomposition theorems, and additive combinatorics.
报告五：
主讲人：杨磊(新加坡国立大学)
Title: Mini course on effective equidistribution of unipotent orbits in homogeneous spaces
Abstract: Given a semisimple Lie group G and its lattice H, we will consider dynamics of group actions on the homogeneous space G/H. Given a one-parameter unipotent subgroup U, we are interested in the distribution of U-orbits in G/H with a quantitative control. In the mini course, I will report recent developments on the study of quantitative equidistribution of unipotent orbits in homogeneous spaces, namely, the effective version of Ratner’s equidistribution theorem. I will start with a brief overview of the topic and related results. Then I will explain a general framework based on a bootstrapping argument. Finally I will give the proofs for several special cases. From the proofs we will see how this problem is related to other interesting topics including decoupling inequalities in harmonic analysis, incidence geometry, and the Balog-Szemerédi-Gowers theorem from additive combinatorics.
报名方式及录取
1.报名方式
扫描以下二维码或者通过链接https://v.wjx.cn/vm/wnJjylo.aspx# 填写报名信息。此外，博士后、在读博士研究生、硕士研究生需提供导师推荐表
请点击链接下载），高年级本科生需提供学院/系/所专家推荐表。推荐表上传至清华云盘https://cloud.tsinghua.edu.cn/u/d/f13413181e1246e0af8a/;文件命名统一格式为“动力系统暑期讲习班推荐表+姓名+学校”
2.截止日期：2026年6月10日
3.录取通知：录取结果将于2026年6月15日后，通过网站和邮件通知学员。
报名二维码：
相关费用及考核
1）为校外学员提供餐费补贴，住宿费用按每间标准房住2位学员的标准报销，人均不超过350元一晚，为京外本科生报销往返路费，其他费用自理。
2）学员需积极参与课程学习，并至少参加一门课程的考试。
组织者：微分方程与动力系统年会学术委员会(主席：叶向东)
承办方：薛金鑫，清华大学数学系
资助方：新基石科学基金会
会务组联系方式：
汪佩洁 62782327 wangpeijie1@tsinghua.edu.cn
清华大学数学科学系
2026年5月
