●INTRODUCTION
1. Organizers刘家成,香港中文大学数学系, kslau@math.cuhk.edu.hk, (0852)26035802(office)
文志英, 清华大学数学系, wenzy@tsinghua.edu.cn, (0086)10 62788976，13911045006
2. Introduction
The main theme of this program is around the study of the geometric structure of various sets and measures in the Euclidean spaces. There will be a strong emphasis on “small irregular” sets of fractal nature. As well known, such sets often abound in dynamical systems, number theory, probability theory, complex analysis, and many other fields. For this reason, experts of different research fields will be invited to introduce the most recent developments, and inter-fields research cooperation will be highly encouraged. During this program (from July 1 to December 31), there will be a series of lectures, a “research seminar” (once a week) and a “student seminar” (twice a week). It is expected that essential progress will be made in the study of Self-similar sets with overlap, Differential equation on fractals, Spectra of operators, Heat-kernel estimation, metric Diophantine approximation, and dimension theory of dynamical systems, etc. Last but not least, it is hoped that our students can be brought to the forefront of geometric measure theory and related research fields.
3. Tentative Participants
Faculty members:
- Xinggang He (Normal Univ. of Central China)
- Jiaxing Hu (Tsinghua Univ.)
- Yong Lin (People’s Univ. of China)
- Qinghui Liu (Beijing Institute of Technology)
- Jihua Ma (Wuhan Univ.)
- Li Peng
- Bo Tan
- Zhixiong Wen
- Jun Wu
- Sanguo Zhu (Huazhong Univ. of Science and Technology)
- Hui Rao (Tsinghua Univ.)
- Huojun Ruan (Zhejiang Univ.)
- Shengyou Wen (Hubei Univ.)
- Min Wu (South China Univ. of Technology)
- Lifeng Xi (Wanli Univ.)
- Yuanling Ye (South China Normal Univ.)
- G.. David(Orsay)
- T. Douqesne(Paris VI)
- K. Falconer (St Andrew )
- A. H. FAN (Amiens)
- A. Grigoryan (Bielefeld)
- S. ITO(Tokyo)
- T. Kamae（Osaka）
- Q. S. LIU(Rennes)
- Pertti Mattila (Helsinki)
- D.Mauldin(North Texas)
- S.M. NGAI(South Georgia)
- J. PEYRIERE (Orsay)
- K. SIMON(Budapest)
- Y. WANG(MSU)
- Y. M. XIAO(MSU)
- Lai-Sang Young (Courant Institute of Mathematics)
- Tianjia Ni
- Ying Xiong
- Yuxia Dai
- Juan Den
- Sheng Fan
- Jinjun Li
- Meiyiong Lv
- Zhihui Yuan
- Xuan Zhao
Research seminar: Every Thursday, 15:00, MCM 705
- Xingang He: Spectral sets and Spectral measures
- Qinghui Liu: Spectra of Schordinger Operators
- Jihua Ma: Almost sure convergence (I)
- Huojun Ruan: Bi-Lip Equivalence of Self-similar sets
- Bo Tan: Combinatorics on Words
- Shengyou Wen: Quasi-symmetric mappings and doubling measures
- Jun Wu: Almost sure convergence (II)
This is the first part of a survey of known results about spectral sets and spectral measure. An emphasis is put on sets of fractal nature, and on the interplay between harmonic analysis and geometric measure theory.
Link: International Workshop on Dynamics and Factals
●PAPERS
Lecture of Marianna Csornyei (2009-12-13)
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Lecture of Alexander Grigoryan (2009-12-8)
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●REPORTS