Organizers:	F.Haslinger (Universität Wien), E-Mail: Friedrich.Haslinger@univie.ac.at
	H.Upmeier (Universität Marburg), E-Mail: Upmeier@Mathematik.Uni-Marburg.de

Time: August - November 1999

There are three main topics in the activity:

1. Weakly pseudoconvex domains of finite type in Cⁿ.

Weakly pseudoconvex domains of finite type were introduced in the attempt to generalize results and methods of the well understood case of strictly pseudoconvex domains, important special topics in this connection are: boundary behavior of the Bergman and Szegö kernel, investigation of the corresponding d-bar-Neumann problem, analytic hypo-ellipticity of pseudo-differential operators, CR-functions and manifolds.

2. Analysis on symmetric domains, discrete series representations and generalizations to non-pseudoconvex domains.

The modern representation theory of semisimple Lie groups uses complex analysis in an essential way. For example the discrete series can be realized in a uniform way via Dolbeault cohomology spaces on the underlying (convex) symmetric domains. Even more challenging is the generalization to non-convex pseudo-concave domains, leading to new types of Hardy and Bergman spaces closely related to twistor theory. The determination of the corresponding Szegö and Bergman kernels in terms of integral geometry is an active research area of great importance, e.g. to the Gelfand-Gindikin program (which expresses the character formulas of harmonic analysis in a uniform way, using Cauchy type >integral formulas). In interaction with topic 1.) of the workshop, the consideration of pseudo-concave symmetric (or tube) domains may bring new insights about Bergman kernels on general non-pseudoconvex domains.

3. Berezin quantization of complex phase spaces, Toeplitz and Hankel operators.

This very active research area at the crossroads of complex analysis and operator theory studies canonical operators associated with the Bergman and Hardy projections. The algebraic structure of these operators reflects deep geometric and complex analytic properties of the underlying domains. For example the compactness of the d-bar-Neumann operator (an important feature of finite type domains, cf. topic 1.) can be determined algebraically from the Toeplitz operator algebra, and using finer tools from operator algebras (composition series, foliation algebras), one can construct sophisticated invariants of complex domains and their boundary which occur naturally e.g. in the class of generalized Reinhardt domains. Very recently, these studies have been extended to the non-pseudoconvex setting involving "non-commutative" Hardy spaces, and a close interaction with topic 2.) is expected.

This program takes place at the same time as the program Applications of Integrability

Participants for whom the time of visit has already been fixed: >

A. Alldridge	11.09. - 02.10.
J. Arazy	01.09. - 30.09.
D. Barrett	22.08. - 04.09.
L. Coburn	13.11. - 28.11.
K. Diederich	19.09. - 03.10.
J. Duval	01.11. - 06.11.
R. Dwilewicz	10.11. - 18.11.
P. Ebenfelt	10.11. - 20.11.
M. Englis	14.11. - 20.11.
J.E. Fornaess	18.09. - 25.09.
G. Francsics	01.10. - 25.10.
B. Gaveau	13.08. - 25.08.
L. Geatti	11.10. - 17.10.
J. Globevnik	26.09. - 03.10.
P.C. Greiner	10.08. - 31.08.
U. Hagenbach	06.10. - 27.10.
G. Herbort	29.08. - 04.09.
A. Iordan	21.08. - 28.08.
D. Kalinin	20.09. - 01.10.
J. Kamimoto	10.10. - 18.10.
M. Kolar	10.11. - 20.11.
A. Koranyi	07.08. - 17.08.
S. Krantz	03.10. - 09.10.
B. Kroetz	14.08. - 22.08.
B. Lamel	13.11. - 20.11.
J. Leiterer	12.09. - 19.09.
I. Lieb	12.09. - 26.09.
K.H. Neeb	06.09. - 24.09.
Y. Neretin	07.09. - 30.09.
N. Nikolov	11.11. - 18.11.
T. Ohsawa	12.09. - 29.09.
B. Orsted	11.10. - 23.10.
P. Pflug	29.08. - 04.09.
M. Schlichenmaier	26.09. - 16.10.
A. Sergeev	11.10. - 01.11.
N. Shcherbina	28.08. - 04.09.
B. Stensones	26.09. - 03.10.
E. Straube	14.11. - 20.11.
D. Tartakoff	01.10. - 10.10.
A. Tumanov	18.08. - 01.09.
A. Unterberger	01.09. - 21.09.
H. Upmeier	15.08. - 30.09.
V. Vajaitu	20.11. - 27.11.
J. Wolf	30.09. - 21.10.
T. Wurzbacher	31.08. - 18.09.
G. Zampieri	05.11. - 12.11.
G. Zhang	16.08. - 27.08.