# Seminarier 1997/98

27 augusti 1997
KASS-gruppen
Planering av höstens verksamhet
11 september 1997
Yasha Eliashberg, Stanford University, USA
Topology of 2-knots and Symplectic geometry
12 september 1997
Yasha Eliashberg, Stanford University, USA
Contact Structures on 3-manifolds
17 september 1997
Bo Berndtsson
Asymptotically holomorphic funtions in several variables. (Joint with M. Andersson.)
24 september 1997
Nikolay Shcherbina
Pseudoconcave pluripolar sets in C2 (after N. Levenberg & Z. Slodkowski).
1 oktober 1997
Nikolay Shcherbina
Pseudoconcave pluripolar sets in C2 (after N. Levenberg & Z. Slodkowski), cont'd.
8 oktober 1997
Non-holomorphic functional calculus for several commuting operators.
This is a continuation of the KASS seminar 17/9, but no precise memories from this talk will be required. Let a1,...,an be bounded operators on a Banach space, with joint spectrum \sigma(a)\subset Cn. We discuss the resolvent \omegaz-\alpha, which is an operator-valued Dolbeault cohomology class in Cn\ \sigma(a). In the case when \sigma(a)\subset Rn and with a certain growth condition on ||\omegaz-a|| we can extend the wellknown holomorphic functional calculus to a larger one, containing nonholomorphic functions. In particular, we present a sharp condition for the existence of a non-quasianalytic functional calculus.
15 oktober 1997
Nikolay Shcherbina
A non-removable generic 4-ball in the unit sphere of C3 (joint with B. Jöricke)
22 oktober 1997
Nikolay Shcherbina
A non-removable generic 4-ball in the unit sphere of C3 (joint with B. Jöricke), continued
29 oktober 1997
Johan Karlsson
The Montessus de Ballore theorem in several variables
It has long been known that the Montessus de Ballore theorem on convergence of rational interpolants is only true in one dimension. None the less a candidate for the name has recently been proved. The trick should sound familiar to numerical analysts: Instead of interpolating, obtain a least squares solution of an unsolvable interpolation problem.
19 november 1997
Bo Berndtsson
Komplex dynamik i flera variabler (efter Mattias Jonsson)
26 november 1997
Bo Berndtsson
Komplex dynamik i flera variabler (efter Mattias Jonsson), forts.
3 december 1997
Simplexfunktionaler och Fantappiètransformen
10 december 1997
Simplexfunktionaler och Fantappiètransformen, forts
22 januari 1998
Aline Bunami, Université d'Orleans
TBA
23 januari 1998
Thomas hansson
Disputation: On Represenation Theorems for Hardy Spaces in Several Complex Variables.
28 januari 1998
Bo Berndtsson
Ickeexistens av Leviplatta hyperytor i P2 (efter Ohsawa-Sibony).
11 februari 1998
Nikolay Shcherbina
The Dirichlet problem for Levi-flat graphs over unbounded domains (Joint with G. Tomassini)
18 februari 1998
Nikolay Shcherbina
The Dirichlet problem for Levi-flat graphs over unbounded domains, continued
18 mars 1998
Mats Aigner
The Ginzburg-Landau vortex equation in R2
1 april 1998
Jie Xiaou, Uppsala
The Qp corona theorem.
For p\in (0,1), let Qp be the subspace of Möbius bounded functions in the Dirichlet type space. Based on the study of multipliers on Qp we establish the corona theorem for Qp.
14 april 1998
John Wermer, Brown University
Linking numbers and boundaries of analytic varieties.
21 april 1998
Finnur Larusson, Western Ontario
Holomorphic functions of slow growth on nested covering spaces of complex manifolds.
22 april 1998
G. Tomassini, Scuola Normale Superiore (Pisa)
Subsets of C2 and Parabolic Problem for the Levi Equation
24-26 april 1998
Nordan-98
29 april 1998
Smooth CR-maps
6 maj 1998
Andrei Domrin, Moskva
Holomorphic functions and embedded real surfaces (after S. Nemirovski)

The talk is devoted to the study of necessary and sufficient topological conditions for an embedded real surfaceto lie in a strictly pseudoconvex domain on a complex surface. These results are used to construct Stein domains on algebraic manifolds and to describe envelopes of holomorphy of real surfaces in CP2 and in some other complex surfaces.

13 maj 1998
Nikolay Kruzhilin, Moskva
Realization in C2 of Stein surfaces fibered over a disc.

The problem of the realization of a Stein manifold fibered over a planar domain as a (fibered) subdomain of a linear space is discussed. An example of a 2-dimensional manifold fibered by discs but not equvialent to a subdomain of C2 is constructed.

14 maj 1998
Jeff McNeal, Ohio State University
Global regularity of the $\bar\partial$-Neumann problem
15 maj 1998
Henrik Delin
Disputation: Weighted Estimates in Complex Analysis and some Inequalities in Riemannian Geometry

This thesis deals with problems from two different fields of mathematics in the four included papers. The first two papers treat problems from harmonic analysis on Riemannian manifolds. Papers 3 and 4 give weighted estimates related to the $\bar\partial$ equation in several complex variables, and should be considered the main part of this thesis.