Selected abstracts for the spring semester 2006:

COLLOQUIUM: Friday, January 20, 2006, 4:00-5:00 p.m., VV B239. 
Fedor Nazarov, Michigan State University.Transportation to random zeroes 
by the gradient flow.



Abstract:
We show that basins of zeroes of a random Gaussian analytic function 
partition the complex plane into domains of equal area and the 
probability that a given basin has diameter greater than R decays 
exponentially in R. This is joint work with M. Sodin and A. Volberg. 

UPCOMING (note some changes below:)==================================================

Tuesday, February 7, 2006, 4:00-5:00 p.m., VV B139.
Alexander Stokolos, De Paul University

Title: On boundary behavior of harmonic and analytic functions

Abstract: This is a joint work with Fausto di Biase, Olof Svensson and
Tomasz Weiss. We study bounded harmonic and analytic functions defined on
the unit disc and their boundary behavior along tangential approach region
whose shape may change from point to point, thus solving a problem posted
by W.Rudin in 1979 and completing picture given by the basic theorems of
Fatou (1906), Lindeloef (1915), Littlewood (1927) and Nagel&Stein (1984).

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Tuesday, February 28, 2006, 4:00-5:00 p.m., VV B139. 
Vladimir Temlyakov (University of South Carolina)

Title: Greedy algorithms with respect to bases


I'll discuss approximation properties of greedy algorithms
with respect to the classical bases (trigonometric, Haar) and with respect
to general bases. The class of greedy bases will be introduced and
discussed.

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Monday, March 6, 4 p.m. vv B239
COLLOQUIUM 
Vladimir Temlyakov (University of South Carolina)


Title: Greedy approximation in Hilbert spaces

Abstract:

I'll talk about greedy algorithms with regard to a general redundant
(overcomplete) system. The questions of convergence and rate of
convergence will be discussed.

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Tuesday, March 7, 4:00-5:00 p.m., VV B139.
Sergey Tikhonov (Centre de Recerca Matematica, Barcelona)

"Convergence of trigonometric series"

Abstract : We discuss three new convergence criteria (for p=\infty, 1<p<\infty, and
p=1) of belonging of sums of trigonometric series to L_p. One-dimensional
and multi-dimensional cases are examined. We also study Hardy-Littlewood
type theorem for multiple trigonometric and Walsh series in L_p with
Muckenhoupt-type weights.


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Tuesday, April 4, 2006, 4:00-5:00 p.m., VV B139. 
Erlend Fornaess Wold (University of Oslo) 
Proper Holomorphic Embeddings of (open) Riemann Surfaces into C^2.

Abstract: We consider open subets of compact surfaces with finite genus,
and we give some sufficient conditions for an embedded surface in
C^2 to be properly embeddable.  These conditions will enable us to embed
all finitely connected planar domains properly into C^2.  If M is an
embedded surface that is also polynomially convex, we may also embedd
arbitrarily small perturbations of M properly.  If time admits, we will
briefly discuss how one in the case of a torus can pass from arbitrarily
small perturbations to all surfaces.


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Tuesday, May 2, 2006, 4:00-5:00 p.m., VV B139. 
Andreea Nicoara (Harvard University)
The Kohn Algorithm in More General Classes of Functions.





Abstract: In 1979 Joseph J. Kohn introduced an algorithm that yields ideals of subelliptic
multipliers which measure whether there is gain in regularity of the 
solution of the dbar-Neumann problem on a pseudoconvex domain in complex n-space. If such 
a domain is defined by a real analytic function, subellipticity of the dbar-Neumann problem is 
equivalent to the Kohn algorithm generating the entire ring of real analytic functions. I 
will discuss what happens to this equivalence for local rings of functions that are strictly 
larger than the local ring of real analytic functions, in particular the local rings of 
the Denjoy-Carleman (quasianalytic) classes of functions.