Several Complex Variables, Analysis on Complex Lie groups and Homogeneous Spaces

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Time : Oct.17-Oct.29,2005
Place: CMS,Zhejiang University,Hangzhou,China

Scientific and Organizing Committees

It is organized by Zhejiang University, Chinese Academy of Science, Beijing and University of Angers, France (with support from the French Embassy inP.R. China). Scienti?c direction:

J. Hilgert (University of Padderborn, Germany),

A. Huckleberry (University of Bochum, Germany),

J.-J. Loeb (University of Angers, France),

G. Roos (St Petersburg, Russia),

A. Sergeev (Steklov Insti-tute, Moscow, Russia),

Zhou Xiangyu (Institute of Mathematics, AMSS, CAS, Beijing and Zhejiang University).


Local organizers


Chen Jiechen (Faculty of Sciences, Zhejiang Univer-sity),

Xu Hongwei (Center of Mathematical Science, Zhejiang University),

Zhou Xiangyu (Institute of Mathematics, AMSS, CAS and Zhejiang University).

The main purpose of the workshop is to provide access to recent develop-ments in the ?eld, for doctoral students and young researchers. There will be ?ve series of lectures of 8h each, whose contents is summarized below. Pre-requisites for the lectures are basic knowledge in Several Complex Variables, Di ? erential Geometry and Lie Groups. The lectures will occupy approxima-tively 4h per day. The remaining time will be devoted to discussion sessions or talks by participants.

The working language will be English. A text of the lecture notes will be available for participants, in printed or electronic form, at the beginning of the workshop.

List of lectures:

1. J. Hilgert (University of Padderborn, Germany) Representation theory in complex geometric settings I.

2. A. Huckleberry (University of Bochum, Germany) Representation theory in complex geometric settings II.

3. J.-J. Loeb (University of Angers, France) On complex automorphisms and holomorphic equivalence of domains.

4. G. Roos (St Petersburg, Russia) Exceptional bounded symmetric domains, Jack polynomials, Dunkl operators.

5. A. Sergeev (Steklov Institute, Moscow, Russia) Seiberg-Witten equations and pseudo-holomorphic curves.

Contents of lectures :

1. and

2. These two strongly integrated courses will provide foundational results, describe basic guiding problems and indicate certain recent develop-ments. The following outline gives a rough indication of the contents.

Introduction to Hardy spaces and to the geometry of actions on ?ag manifolds.

Realization of unitary representations on Hardy and weighted Bergman spaces.

Uniform realization of all holomorphic discrete series representations as the irreducible components of a Hardy space.

Representations associated to cycle spaces of orbits in ?ag manifolds.

3. The following topics will be covered

Generalization of the classical Schwarz lemma to bounded domains in C n .Extension to Kobayashi hyperbolic manifolds. Role of pseudo-convexity.

Using pseudo-convexity in the case of non hyperbolic manifolds. Only a few results are known in this direction and there are many open questions.

4. We give a presentation of exceptional bounded symmetric domains using the Albert algebra and exceptional Jordan triple systems. In the last chapter, we give some facts about Jack polynomials and associated di ? erential-di ? erence operators. We then give their explicit form in the case of exceptional symmetric domains.

5. The main content is the relation between Seiberg-Witten equations on 4-dimensional symplectic (and though almost complex) manifolds and pseudo-holomorphic curves. This relation is established through a limiting construc-tion, due to Taubes, and has a non-trivial 3-dimensional analogue, related to Ginzburg-Landau equations, arising in the superconductivity theory.

If you have any questions about the workshop,
please contact us:

Chen Jing :cj@cms.zju.edu.cn

Ke-Mei Shen :skm@cms.zju.edu.cn

Please register at Oct.16,2005

Address:Zhejiang University, Yuquan Campus

Center of Mathematical Science, 313 room.(for students)

Address:Ling Feng Shan Zhuang(for Professor)

?¡ª¡·How to get to CMS at Zhejiang University, Yuquan Campus?

1 From Hangzhou Xiao-Shan Airport, take an airport shuttle (20RMB/person) to Wulin Gate, and then either take a taxi or Bus line #28 (or 21) to Zhejiang University, Yuquan Campus.

2 From Hangzhou Train Station, take a taxi or Bus line #21 to Zhejiang University, Yuquan Campus.

3 From Hangzhou Eastern Train Station, take a taxi or Bus line #28 to Zhejiang University, Yuquan Campus.

4 From Hangzhou Long-distance Bus Station, take a taxi to Zhejiang University, Yuquan Campus.

5 From Shanghai Hongqiao Airport, take an airport shuttle (85RMB/person) to Wulin Gate, then either take a taxi or Bus line #28 (or 21) to Zhejiang University, Yuquan Campus.

6 From Beijing, Hongkong or any other city, take a flight from your city to Hangzhou Xiao-Shan Airport, and then take an airport shuttle (20RMB/person) to Wulin Gate. At Wulin Gate, either take a taxi or Bus line #28 (or 21) to Zhejiang University, Yuquan Campus.

7 From Shanghai Pudong Airport to Dragon Sports Center (which is near our campus) : 10:30 12:00 13:30 15:30 17:30 19:00
From Dragon Sports Center to Shanghai Pudong Airport: 7:00 8:30 10:30 12:30 14:30 16:00
Consultative Telephone: 0571-87990788¡¢96123
(100RMB/person)

8 From Shanghai Pudong Airport, take an airport shuttle (85RMB/person) to Wulin Gate , and then either take a taxi or Bus line #28 (or 21) to Zhejiang University, Yuquan Campus.

Schedule (From Shanghai Pudong Airport to Wulin Gate)

Shanghai Pudong Airport £­>Wulin Gate

am 8£º40£¬10£º10£¬11£º40

pm 1£º10£¬2£º40£¬4£º10£¬5£º50

Wulin Gate£­>Shanghai Pudong Airport

am 6£º00£¬7£º30£¬9£º00£¬10£º30£¬12£º00

pm 1£º30£¬3£º00£¬4£º00

Remark£º From Shanghai Pudong Airport to Wulin Gate,if you arrive in Shanghai before pm7:00 , you can call the driver to wait for you in Pudong airport. Telephone£º13916108450£¨Mr. Jiang£©


How to take the airport shuttle:

The Bus Station is located in a car park opposite the arrival hall. There is a passage link which can be accessed in the second level (2nd floor) of the arrival hall. You need to go through the passage link and take an elevator down to level 1A. Then you will see a car park and the bus station (a small and low-rise building).

Below is for CMS's Chinese address and telephone number. You can print it and show to the local taxi driver, which is very useful to get to CMS from Dragon Sports Center or any other places in Hangzhou successfully!

Below is for Dragon Sports Center's Chinese address and telephone number. You can print it and show to the local taxi driver, which is very useful to get to Dragon Sports Center from CMS successfully!

Below is the map of Zhejiang University, Yuquan Campus: (You can download it to see it clearly.)

 

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Address: Mailbox 1511, Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

  Phone: 0086-571-87953030, Fax: 0086-571-87953035,