日期	时间	报告人及题目		主持人
开幕式	8:00-8:20	开幕式 岚桥锦江大酒店国际会议中心二层北侧五号会议室     ）		孟凡伟 2022白菜注册网站
	8:20-8:30	照相
会场	岚桥锦江大酒店国际会议中心二层北侧五号会议室
4月15日上午	8:30-9:20	王跃飞 深圳大学	On Conformal Restriction Measures	乌兰哈斯 汕头大学
	9:20-10:10	崔贵珍 中科院、深圳大学	Invariant graphs in Julia sets and decomposition of rational maps
	10:10-10:30	茶歇
	10:30-11:20	戎锋 上海交通大学	The Burns-Krantz rigidity with an interior fixed point	邱维元 复旦大学
	11:20-12:10	杨飞 南京大学	Julia sets with positive area and Mane conjecture
4月15日中午	12:10-13:30	午餐（酒店主楼一层东首瑞泰西餐厅）
4月15日下午	14:00-14:50	程涛 华东师范大学	Quasisymmetry of quasiconformal homeomorphisms in Loewner space	黄曼子 湖南师范大学
	14:50-15:40	潘会平 华南理工大学	Ray structures on Teichmuller spaces
	15:40-16：00	茶歇
	16:00-16:50	王轶珉 上海师范大学	The full renormalization horseshoe for real box maps with minimal post-critical sets	王晓光 浙江大学
	16:50-17:40	杨璐鲜 深圳大学	Renormalizations of rational maps from stable multicurves
4月15日晚上	18:00-21:00	晚宴（酒店主楼二层中餐厅南海厅）

 

会场	岚桥锦江大酒店国际会议中心二层北侧五号会议室
4月16日上午	8:30-9:20	廖良文 南京大学	Complex differential equations and related topics.	扈培础 山东大学
	9:20-10:10	张慎行 复旦大学	A comparison between Avila-Gouëzel-Yoccoz norm and Teichmüller norm
	10:10-10:30	茶 歇
	10:30-11:20	张艳华 2022白菜注册网站	Local connectivity of Julia sets for rational maps with Siegel disks	叶和溪 浙江大学
4月16日中午	11:30-13:30	午 餐（酒店主楼一层东首瑞泰西餐厅）
4月16日下午	自由活动
4月16日晚上	18:30-20:00	晚餐（酒店主楼一层东首瑞泰西餐厅）

报 告 摘 要

王跃飞

题目: On Conformal Restriction Measures

摘要: We will talk about our recent results on conformal restriction measures. This is joint work with Y. Han and M. Zinsmeister.

 

 

崔贵珍

题目: Invariant graphs in Julia sets and decomposition of rational maps

摘要: I will present a recent result joint with Y. Gao and J. Zeng. We prove that a post-critically finite rational map has an -invariant graph in the Julia set. The proof involves a decomposition of rational maps.

 

 

戎锋

题目: The Burns-Krantz rigidity with an interior fixed point

摘要: We first give a brief survey on the Burns-Krantz rigidity, highlighting Huang’s work on the rigidity with an interior fixed point. Then, we present some of our recent results, in particular the solution of Huang’s conjecture.

 

 

杨飞

题目: Julia sets with positive area and Mane conjecture

摘要: The proofs of the existence of quadratic polynomials having Julia sets with positive area, are recent important breakthroughs in one-dimensional complex dynamics. In the work of Buff-Cheritat and Avila-Lyubich, a crucial ingredient is the control of post-critical sets of quadratic polynomials by using Inou-Shishikura's invariant class.

By means of near-parabolic renormalization techniques, we generalize the positive area results to all meromorphic functions in a class introduced by Shishikura in 1998 (which is an invariant subclass of Inou-Shishikura's). Our proof shows that, for these maps having a Cremer point or Siegel disk of certain rotation numbers, the set of points in the Julia set whose forward orbits stay near the post-critical set already occupies the positive area. As a by-product, this leads us to prove the existence of a rational map for which the Julia set is the whole Riemann sphere while the map is not ergodic with respect to the Lebesgue measure, which settles a conjecture of Mane from 1985 in the negative.

Moreover, based on the invariant classes recently constructed by Cheritat and the same techniques, we prove the existence of Julia sets with positive area in unicritical polynomials of any degree.

 

 

程涛

题目: Quasisymmetry of quasiconformal homeomorphisms in Loewner space

摘要: This talk is devoted to the study of a fundamental problem in the theory of quasiconformal analysis: under what conditions local quasiconformality of a homeomorphism implies its global quasisymmetry. In particular, we introduce the concept of weak (L,M)-quasisymmetry, serving as a bridge between local quasiconformality and global quasisymmetry. We show that in general metric spaces local regularity and some connectivity together with the Loewner condition are sufficient for a quasiconformal map to be weakly (L,M)-quasisymmetric, and subsequently, quasisymmetric with respect to the internal metrics.

 

 

潘会平

题目: Ray structures on Teichmuller spaces

摘要: Teichmuller space admits several ray structures, such as the Teichmuller geodesic ray, Thurston stretch ray, harmonic map (dual) ray, grafting ray, etc. In the first part of this talk, we will depict harmonic map ray structures on Teichmuller space as a geometric transition between Teichmuller ray structures and Thurston geodesic ray structures. In particular, by appropriately degenerating the source of a harmonic map between hyperbolic surfaces, the harmonic map rays through the target converge to a Thurston geodesic; by appropriately degenerating the target of the harmonic map, those harmonic map dual rays through the domain converge to a Teichmuller geodesic. In the second part, we will discuss applications to Thurston metric. While there may be many Thurston metric geodesics between a pair of ordered points in Teichmuller space, we select a unique Thurston geodesic through those points in a canonical way. This allows us to define two versions of geodesic flows under the Thurston metric. This is a joint work with Michael Wolf (arXiv: 2206.01371).

 

 

王轶珉

题目: The full renormalization horseshoe for real box maps with minimal post-critical sets

摘要: Deep renormalizations of infinitely renormalizable multimodal maps can be naturally treated as real box maps with minimal post-critical sets. In this talk, we show the existence of the full renormalization horseshoe for real box maps with minimal post-critical sets. Moreover, the renormalization operator contracts exponentially fast along the hybrid leaves.

 

 

杨璐鲜

题目: Renormalizations of rational maps from stable multicurves

摘要: For a class of postcritically finite rational maps with specific combinatorial property, we find disjoint type renormalizations. We also construct rational maps satisfying the specific combinatorial property by tuning-folding surgery.

 

 

廖良文

题目: Complex differential equations and related topics.

摘要：In this talk，we will introduce  recent results about complex Schwarzian differential equations and complexBriot-Bouquet differential equations.

 

 

张慎行

题目: A comparison between Avila-Gouëzel-Yoccoz norm and Teichmüller norm

摘要: In 2006, Avila, Gouëzel and Yoccoz defined a norm on any stratum of Abelian differentials. We give a comparison between the Avila-Gouëzel-Yoccoz norm and the Teichmüller norm on the principal stratum of holomorphic quadratic differentials.

 

 

张艳华

题目: Local connectivity of Julia sets for rational maps with Siegel disks

摘要: We prove that a long iteration of rational maps is expansive near boundaries of bounded type Siegel disks. This leads us to extend Petersen's local connectivity result on the Julia sets of quadratic Siegel polynomials to a general case. A new key feature in the proof is that the puzzles are not used. This is a joint work with Shuyi Wang, Fei Yang and Gaofei Zhang.