一、会 议 日 程

4月25日上午8:00-11:50 学术报告 （地点：科技楼二楼南会议室）
时间	报告人及题目			主持人
8:00-8:30	开幕式、合影			王培合 （age动漫 ）
8:30-9:15	范爱华 武汉大学		Fractal and   Multifractal Problems in Infinite-Dimensional Spaces	王跃飞 深圳大学
9:15-10:00	王晓光 浙江大学		横截性	崔贵珍 深圳大学
10:20-11:05	李智强 北京大学		Computable analysis in complex analysis   and dynamics	伍胜健 北京大学
11:05-11:50	杨飞 南京大学		Local connectivity of Julia sets of some   transcendental maps with Siegel disks	张广远 清华大学
4月25日下午14:30-17:05 学术报告 （地点：科技楼二楼南会议室）
14:30-15:15		周泽 深圳大学	Morse theory and moduli spaces of self-avoiding polygonal   linkages	漆毅 北京航空航天大学
15:15-16:00		潘会平 华南理工大学	Counting Saddle Connections on   Hyperelliptic Translation Surfaces with a Slit	沈玉良 苏州大学
16:20-17:05		黄可平 哈尔滨工业大学	Compositional independence for polynomial-like   maps	尹永成 浙江大学
4月26日上午8:00-11:30 学术报告 （地点：科技楼二楼南会议室）
8:30-9:15		罗旭丹 中国科学院	Obliquely interacting solitary waves and wave   wakes in free-surface flows	扈培础 山东大学
9:15-10:00		付宇铭 深圳大学	Mating Mandelbrot set with laminations of Siegel quadratic   polynomials	廖良文 南京大学
10:10-11:30		自由学术讨论
4月26日下午14:00-18:00 学术报告 （地点：科技楼二楼南会议室）
14:00-18:00		自由讨论、离会

二、学 术 报 告

报告人：范爱华（武汉大学）

题目: Fractal and Multifractal Problems in Infinite-Dimensional Spaces

摘要:

Classical fractal and multifractal theory has largely focused on objects in finite-dimensional spaces. How should one deal with objects in infinite-dimensional spaces? The law of Brownian motion is a Borel probability measure supported on the infinite-dimensional space , and its local behavior exhibits multifractal features. This can be quantified using scale, a notion more general than dimension. These results were obtained in joint work with Mathieu Helfter, where we derived the first multifractal spectrum for a measure on an infinite-dimensional space. This is still a largely unexplored area: the distributional measures of random processes remain to be studied, especially Gaussian measures on Hilbert and Banach spaces. We will present open problems in this direction.

报告人简介：范爱华，法国Picardie大学特级教授，武汉大学特聘教授，获国家级高层次人才计划支持，获国家基金委海外合作基金（中科院数学所）。博士毕业于法国南巴黎大学（现为University of Paris-Saclay)，师从法国科学院院士Kahane教授。曾任华中师范大学特聘教授, Wallenberg访问教授 (瑞典隆德大学)。主要研究方向：动力系统与遍历理论，傅立叶分析，几何测度论，概率论与随机混沌等。

报告人：付宇铭（深圳大学）

题目：Mating Mandelbrot set with laminations of Siegel quadratic polynomials

摘要：In this talk, we introduce a topological construction that glues together two points on the boundary of the Mandelbrot set whose external angles correspond to equivalent points in the lamination of the Siegel quadratic polynomial with a given external angle. This yields a quotient space of the quadratic polynomial space. It can be shown that the image of the Mandelbrot set under this quotient map is locally connected. This topological construction is called the mating of the Mandelbrot set with a lamination. This construction is closely related to the study of the parameter space of quadratic rational maps with a bounded-type Siegel disk.

报告人简介：深圳大学专职副研究员，研究领域为复动力系统。于2021年博士毕业于南京大学，之后在深圳大学从事博士后研究。

报告人：黄可平（哈尔滨工业大学）

题目: Compositional independence for polynomial-like maps

摘要:

We show that if : are polynomial-like maps of topological degrees at least 2 with different equilibrium measures, then for all sufficiently large n, the semigroup under composition is a free semigroup. This proves the main results of the earlier works Bell-Huang-Peng-Tucker and Beaumont in a different case.

报告人简介：黄可平，哈尔滨工业大学数学研究院教授。2020年博士毕业于罗切斯特大学，研究方向算术动力系统和丢番图几何。

报告人：李智强（北京大学）

题目: Computable analysis in complex analysis and dynamics

摘要: We give an overview of the recent developments in the field of computable analysis in connection with complex analysis and dynamics. In particular, we address the challenges arising from nonuniform expansion in the study of computable ergodic theory in complex dynamics.

报告人简介：李智强，北京大学数学学院、北京国际数学中心副教授，国家级青年人才入选者。研究方向为动力系统、度量空间几何与复分析。在Proc. Lond. Math. Soc、Comm. Math. Phys、Adv. Math、Math. Ann、TAMS、IMRN等国际权威数学期刊发表论文多篇，在Springer出版专著一部。

报告人：罗旭丹（中国科学院）

题目: Obliquely interacting solitary waves and wave wakes in free-surface flows

摘要: We investigate the weakly nonlinear isotropic bi-directional Benney-Luke (BL) equation, with a particular focus on soliton dynamics. The associated modulation equations are derived that describe the evolution of soliton amplitude and slope. By analyzing rarefaction waves and shock waves within these modulation equations, we derive the Riemann invariants and modified Rankine-Hugoniot conditions, which help characterize the Mach expansion and Mach reflection phenomena. We also derive analytical formulas for the critical angle and the Mach stem amplitude, showing that as the soliton speed is in the vicinity of unity, the results from the BL equation align closely with those of the Kadomtsev-Petviashvili (KP) equation. Furthermore, as a far-field approximation for the forced BL equation -- which models wave and flow interactions with local topography -- the modulation equations yield a slowly varying similarity solution. This solution indicates that the precursor wavefronts created by topography moving at subcritical or critical speeds take the shape of a circular arc, in contrast to the parabolic wavefronts observed in the forced KP equation.

报告人简介：罗旭丹，中国科学院数学与系统科学研究院副研究员。 博士毕业于香港科技大学，毕业后曾先后在科罗拉多大学博尔德分校和纽约州立大学水牛城分校从事博士后研究。 主要研究兴趣为复分析和非线性波，相关成果发表在Adv. Math., SIAM J. Math. Anal., SIAM J. Appl. Math., J. Fluid Mech., Inverse Problems等国际权威杂志上。

报告人：潘会平（华南理工大学）

题目: Counting Saddle Connections on Hyperelliptic Translation Surfaces with a Slit

摘要: In this talk, we consider saddle connections on a translation surface in a hyperelliptic connected component of a stratum that do not intersect the interior of a distinguished saddle connection. For this restricted set of saddle connections, we show that it satisfies an L(log L)^{d-2} growth rate, where d is the complex dimension of the hyperelliptic stratum. The upper bound holds for all translation surfaces in the hyperelliptic stratum while the lower bound holds for almost every surface in the hyperelliptic stratum. The proof of the lower bound uses horocycle renormalization. This is a joint work with David Aulicino, Howard Masur and Weixu Su.

报告人简介：潘会平2011年本科毕业于华南理工大学电子科学与技术专业（微电子方向），2016年博士毕业于中山大学基础数学专业，2016至2018年在复旦大学从事博士后研究，2022年6月加入华南理工大学数学学院，任准聘副教授。其研究方向是复分析中的Teichmüller理论，主要研究曲面上的复结构、双曲结构、平坦结构等几何结构，以及这些结构之间的形变。相关论文在Acta Mathematica、Mathematische Annalen、Science China Mathematics、Transactions ofthe American Mathematical Society、InternationalMathematics Research Notices等期刊发表或接受发表。

报告人：王晓光（浙江大学）

题目: 横截性

摘要: 横截性理论在复动力系统的高维参数空间的研究中有广泛应用. 本报告介绍参数空间在几何有限有理映射处的横截性.

报告人简介：王晓光于2011年博士毕业于复旦大学，之后曾在中科院数学与系统科学研究院，美国布朗大学ICERM研究所，美国伊利诺伊大学芝加哥分校从事博士后研究. 2012年8月至今,在浙江大学age动漫 工作。主要从事基础数学-复分析与复动力系统的研究，在有理映射的动力学行为，模空间，组合刻画等方面取得了一系列成果. 曾获得国家优秀青年基金, 浙江省自然科学一等奖。主编国家“101计划”核心教材《复变函数》一部。

报告人：杨飞（南京大学）

题目: Local connectivity of Julia sets of some transcendental maps with Siegel disks

摘要:Based on the weak expansion property of a long iteration of a family of quasi-Blaschke products near the unit circle established recently, we prove that the Julia sets of a number of transcendental entire functions with bounded type Siegel disks are locally connected. In particular, if is of bounded type, then the Julia set of the sine function is locally connected. This is a joint work with Gaofei Zhang and Yanhua Zhang.

报告人简介：杨飞，南京大学数学系副教授，研究方向为复动力系统。2013年6月于复旦大学age动漫 获得博士学位，2013年7月至今在南京大学数学系工作。在 J. Eur. Math. Soc., Math. Ann., Int. Math. Res. Not., Trans. AMS, Math. Z., Nonlinearity, Ergod. Th. Dynam. Sys., Sci. China Math. 等数学期刊上发表SCI论文20余篇。已主持国家自然科学基金和江苏省自然科学基金各2项，2022年获国家自然科学基金委优秀青年基金资助。

报告人：周泽（深圳大学）

题目: Morse theory and moduli spaces of self-avoiding polygonal linkages

摘要: We show that a smooth $d$-manifold $M$ is diffeomorphic to $\mathbb R^d$ if it admits a Lyapunov-Reeb function, i.e., a smooth map $f:M\to\mathbb R$ that is proper, lower-bounded, and has a unique critical point. By constructing such functions, we prove that the moduli spaces of self-avoiding polygonal linkages and configurations are diffeomorphic to Euclidean spaces. This provides a refined answer to the Carpenter's Rule Problem and confirms a conjecture proposed by Gonz\'{a}lez and Sedano-Mendoza. Furthermore, we describe foliation structures of these moduli spaces and develop algorithms for the Linkage (Configuration) Refolding Problem. This is a joint work with Te Ba.

报告人简介：周泽，深圳大学教授，国家自然科学基金委优秀青年基金项目入选者，研究方向为复分析与圆堆积。2015年博士毕业于中国科学院数学与系统科学研究院。2015.08-2022.09任职于湖南大学，先后担任副教授与教授。2022年10月起担任深圳大学教授。其主要贡献在于将Teichmullerl理论与微分拓扑方法等工具引入到圆堆积理论的研究，解决了Schutle、Chow-Luo等人提出的一些公开问题，其成果发表于Invent. Math.、Amer. J. Math.、Adv. Math等国际知名数学期刊。曾先后获得钟家庆数学奖及中国新锐人物突出贡献奖等奖励。