Programme on Lie Groups 2001


Stringy Geometry and Topology of Orbifolds

Professor Yongbin Ruan
Hong Kong University of Science and Technology, HK

There is an emerging new subject of mathematics, which we call "Stringy Geometry and Topology of Orbifolds". The motivation of stringy geometry and topology of orbifolds comes from orbifold string theory discovered by physicists Dixon, Harvey, Vafa and Witten more than fifteen years ago. Orbifolds have been around in mathematics since 50's. However, the classical theory of orbifolds is basically an extension of theory of smooth manifolds. The stringy geometry and topology is different. Its main purpose is to study stringy properties of orbifolds, which is unique for orbifolds. Orbifold string theory model is a popular model in string theory. There are more than two hundred papers on hep-th whose titles include orbifold. During last two years, its mathematical counterpart is undergoing rapid development. It is fair to say that new phenomena are being discovered every month! The growth of its foundation and connections to other areas of mathematics is explosive. On the other hand, it is still in its relatively early stage of development. I estimate that less than quarter of physics papers on this subject has been seriously looked at by mathematicians. Therefore, it is a particularly good time to enter this subject now. Unlike other physics inspired theories such as gauge theory and quantum cohomology where entry costs are high, this subject is relatively easy to learn. I will cover basic of this subject aided by large number of examples. Here is the plan
Dates / Time:
A series of 8 lectures on Wednesdays and Fridays to be held 4:00 - 5:30pm, May 16 - June 8, 2001
Room 517, Meng Wah Complex