*September 8, 1999***Alexander Tumanov, University of Illinois, Urbana**- Extremal discs and the regularity of CR mappings in higher codimension.
**Abstract:**We give some details on the geometry of the extremal discs for CR manifolds of higher codimension and prove the following analogue of Fefferman's mapping theorem. Let M and N be smooth strictly pseudoconvex generic CR-manifolds in complex space. Let F be a CR-homeomorphism M to N such that F together with its inverse satisfies a Lipschitz condition with some exponent 0<a<1. Then F is smooth.*September 15, 1999***Bo Berndtsson**- Leviplatta ytor och Seiberg-Wittens ekvationer.
*September 22, 1999***Alexander Brudnyi, Beer-Sheva University, Israel**- Matrix-valued corona theorem and topology of the maximal ideal space of H^\infty.
*September 29, 1999***Bo Berndtsson**- Leviplatta ytor och Seiberg-Wittens ekvationer, forts.
*October 6, 1999***Johan Karlsson**- Nyare resultat om element- och värdeområden för kedjebråk vilka är modellerade på de s.k. regulära (inga förkunskaper om kedjebråk behövs).
*October 27, 1999***Klas Diederich, University of Wuppertal, Germany**- Why are pluricomplex Green functions so useful?
**Abstract:**Several kinds of pluricomplex Green functions for bounded pseudoconvex domains in**C**^{n}will be studied and estimates for them derived. At least two important applications will be presented.*November 3, 1999***Niklas Lindholm**- A necessary condition for sampling in some
generalized Fock spaces in
**C**^{n} **Abstract:**By estimating asymptotically the number of large (close to one) eigenvalues of a certain Toeplitz concentration operator, we will obtain a necessary condition for a uniformly separated sequence in**C**^{n}to be sampling in some weighted spaces of entire functions.*November 10, 1999***Niklas Lindholm**- A necessary condition for sampling in some
generalized Fock spaces in
**C**^{n}(cont. from last week) *December 15, 1999***Yurii Lyubarskii, NTNU, Trondheim**- Approximation of subharmonic functions.
*January 26, 2000***Sergey Kislyakov, St. Petersburg**- Interpolation involving bianalytic functions.
*February 9, 2000***Prof. Valerij Beloshapka, Moscow State University**- Real manifolds in complex space: invariants, automorphisms, classifications
**Abstract:**The problem of holomorphic classification of a domain in a complex space is the problem of classification of its boundary. This boundary is a real submanifold of a complex space. Such manifolds of codimension one were studied by H. Poincaré, E. Cartan, N. Tanaka, S. S. Chern, J. Moser and others. During the last 12 years there was some progress in the study of real submanifolds of higher codimension. One can mention a criteria of finite dimensionality of the automorphisms groups, construction of the set of holomorphic invariants and explicit description of the automorphisms group of tangent quadric.*February 23, 2000***Stephane Rigat, Marseille/Sundsvall**- Explicit version of the fundamental principle in the non homogeneous case and applications to the complex Cauchy problem.
*March-May, 2000***Evgenij Chirka, Moscow**- Course on Selected topics in SCV.
*March 1, 2000***Maria Roginskaya**- On the growth of harmonic and M-harmonic functions in the complex unit ball near the singularities on the boundary.
*March 8, 2000***Roland Wolff, Sarbrücken**- Composition of inner mappings on the ball.
**Abstract:**It is well known that the composition of two inner functions on the unit disc in the complex plane is an inner function again. If $F:B_k\to B_m$ and $G:B_m\to B_n$ are inner mappings on the corresponding unit balls, then in general $G\circ F$ is not inner. But if the Borel measure $\sigma_k^{F^\ast}$ on the sphere $S_m$, \[ \sigma_k^{F^\ast}(A)=\sigma_k\big( [F^\ast]^{-1}(A) \big) \] satisfies $\sigma_k^{F^\ast}=\sigma_m$ (= surface measure on $S_m$), then it was shown by Ding and Sun in 1997 that $G\circ F$ is inner. This solves a problem posed by Walter Rudin in 1986. In this talk an operator theoretic approach to the problem will be presented and it will be proved that the weaker condition $\sigma_k^{F^\ast}\ll\sigma_m$ is sufficient for $G\circ F$ to be inner.*March 15, 2000***Bruno Fabre**- The Abel-Lie theorem
*April 12, 2000***Evgenij Chirka, Moscow**- On Lipschitz graphs which are pseudoconvex from both sides
**Abstract:**It is well known that a smooth real hypersurface in complex space dividing two domains of holomorphy is foliated by complex hypersurfaces. The problems will be discussed for Lipschitz hypersurfaces.*April 19, 2000***Mats Andersson**- Two ways to construct Taylor's functional calculus for commuting operators.
*April 26, 2000***Nikolay Shirokov, St. Petersburg**- A variational formula for the Bergman kernel.
*May 10, 2000***Z. Slodkowski, Chicago**- Canonical models for holomorphic motions.
*May 17, 2000***Mihai Putinar, Santa Barbara**- Spectral localization and applications.
**Abstract:**The first part of the seminar will be a review, based on simple examples, of spectral localization ideas of N. Dunford, E. Bishop and C. Foias.

The second part of the seminar will expand these ideas from one complex variable to several complex variables, with some aid and intuition from complex analytic geometry. Several applications to division problems and computation of index will be discussed.*May 29, 2000***Zbigniew Slodkowski**- Evolution of sets by Levi curvature.

Namn (Name) |
Tidsperiod (Period) |

Evgenij Chirka, Moscow | 000301-000515 |

Nessim Sibony, Paris | 000324-000331 |

Zibigniew Slodkovski, Chicago | 000508-000605 |

Roland Wolff, Sarbrücken | 000302-000331 |