Selected abstracts for the  spring  semester 2007:


Tuesday, February 6, 2007, 4:00-5:00 p.m., VV B139
Brian Street(Princeton)


Abstract:

Recently, Kohn gave an example of a sum of squares of complex vector fields that satisfy
H\"ormander's condition (they and their commutators span the complexified tangent space)
that is hypoelliptic but not subelliptic (this is in contrast to the well-known case of
real vector fields studied by H\"ormander). In this talk, I will discuss a parametrix
construction for Kohn's operator, that yields another proof of hypoellipticity, along
with L^p and Lipschitz regularity.

====================================================
Tuesday, February 27, 2007, 4:00-5:00 p.m., VV B139
Sergey Denissov (UW)
The sharp form of strong Szego theorem for truncated Wiener-Hopf
operators and associated problems of approximation theory.


Abstract: We will show how the theory of Krein systems is applied to various
classical problems of analysis. In particular, we will mention the 
strong Szego theorem for truncated Wiener-Hopf operators 
and characterization of Dirac operators with L^2 potentials.

====================================================
Wednesday, March 14, 2007, 4:00-5:00 p.m., VV B139
Burglind Joericke (University of Stockholm)
Pluripolar hulls and fine analytic continuation 


Abstract:

I will discuss the following question about the structure of
pluripolar sets, the exceptional sets in pluripotential theory. Given
an (open, embedded) analytic disc in C^2 , find its pluripolar hull,
i.e. the set of all points such that any plurisubharmonic function
that is minus-infinity on the disc, is minus-infinity at that
point. It turns out that the problem is related to fine analytic
continuation rather than to analytic continuation. The notion of fine
analyticity appeared some decades ago and uses the fine topology
introduced by Cartan.

====================================================


Tuesday, April 17, 2007,  4:00-5:00 p.m., VV B139
Marius Junge (University of Illinois, Urbana-Champaign)
Noncommutative gradients

Abstract: The theory of semigroups provides us with a natural notion of a
gradient even for noncommutative
objects. More precisely, we will consider the semigroup of positive maps
where the generator is given by the length function of the group. The aim of
this talk is to present a mix of analytic and algebraic tools which allows
us to estimate the norm of the gradient in L_p, p>2. This is a
noncommutative analogue for Stein's classical estimate on Riesz-transforms
for compact groups.