Outline:

The applied analysts, functional analysts, harmonic analysts can be broadly classified as the analysis group. It is another research strength of the department. The Programme on Analysis and Partial Differential Equation (PDE) is based on the common interest of this group. The class of harmonic functions is of central importance in analysis, PDE and probability theory. The new momentum comes from the recent development in differential geometry, fractals and wavelets. Fractals and wavelets are research areas started in the last two decades and have had an explosive development because of their wide range of applications to various discipline areas of sciences and the deep mathematics involved. Interestingly enough they can be treated broadly as harmonic functions with scaling. The study is intended to bring together the classical and the new techniques and to develop them into a coherent area. The PDE part of the programme emphasizes the concentration phenomena from nonlinear elliptic and parabolic equations arising from physical and biological sciences. The direction of PDE on fractals is starting to develop and it is also included in the programme.

Organizing Committee:

• Kai-Seng Chou (Department of Mathematics, CUHK)
• Ka-Sing Lau (Department of Mathematics, CUHK)
• Chi-Wai Leung (Department of Mathematics, CUHK)
• Kung-Fu Ng (Department of Mathematics, CUHK)
• Ping-Kwan Tam (Department of Mathematics, CUHK)
• Jun-Cheng Wei (Department of Mathematics, CUHK)

Scientific Description:

Fractals and Harmonic Analysis: The programme is concentrated on topics related to iterated function systems, dynamical systems, multifractal structure, tiling, PDE on fractals, and the related aspects in harmonic analysis, functional analysis and probability theory. It sponsors short term visitors and longer term postdoctoral fellows from China and abroad. The activities are coordinated with the Mathematics Department with include weekly seminars and lecture series. A workshop is planned in December 4-8, 2000. (For details, please click here.)

Program:

• IMS Lecture Series
1. Dynamical Systems and ergodic Theory

by Prof. Ka-Sing Lau (Dept. of Mathematics, CUHK)and
Prof. Ai-Hua Fan (Faculte de Mathematiques et Informatique, Unversite de Picardie Jules Verne)
Date: Every Wednesday (Sep.22,1999 - Dec. 10,1999)
Time: 4:30pm - 7:00pm
Venue: LT4, Lady Shaw Building, CUHK, Shatin.
 
2. Tauberian Theorems and Some Applications

by Dr. Titus Hilberdink (Goldsmiths College, University of London,England)
Date:October 21, 1999 (Thursday)
Time: 3:00pm - 4:30pm
Venue:Room 232, Lady Shaw Building, CUHK, Shatin.
and
Date: Every Thursday (Oct.28,1999 - Dec.9, 1999)
Time: 4:00pm - 5:30pm
Venue: Room 222B, Lady Shaw Building, CUHK, Shatin.
 
3. Bernoulli Convolutions and Pisot numbers

by Prof. Dejun Feng (Department of Applied Mathematics, Tsinghua University, China)
Date: February 1,2000 (Tuesday)
Time:2:30pm - 4:00pm
Venue: Room 222B, Lady Shaw Building, CUHK, Shatin.
and
Date: Every Tuesday (Feb.15,2000 - March 21, 2000)
Time: 2:00pm - 3:30pm
Venue: Room 222B, Lady Shaw Building, CUHK, Shatin.
 
4. Brownian motion on nested fractals

by Prof. Jun WU (Department of Mathematics, Wuhan University, China)
Date: Every Tuesday (From March 28, 2000 to the end of the this term)
Time: 2:00pm - 3:30pm
Venue: Room 222B, Lady Shaw Building, CUHK, Shatin.

Sponsors:

• The Institute of Mathematical Sciences, CUHK.
• The Department of Mathematics, CUHK.
• The Zheng Ge Ru Foundation.

Enquiry:

Professor K. S. Lau
Email:kslau@math.cuhk.edu.hk

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