ABSTRACTS FOR TALKS IN THE ANALYSIS SEMINAR


Tuesday, April 27, 2004, 4:00 p.m., VV B113
Marius Junge (University of Illinois at Urbana-Champaign)

Birkhoff's maximal inequality in noncommutative L_p spaces

Abstract:
We will  prove the analog of Birkhoff's inequality for
complete positive trace preserving transformations on
noncommutative measure spaces starting from Lance's weak $L_1$
estimate. These weak $L_1$ estimates are weaker then their
commutative analogs and require a refined interpolation technique
for $p>1$. As a consequence the order of the constants in the
noncommutative setting is ultimatively  different. These results
generalize to the nontracial case using Haagerup's cross product
techniques. This is joint work  with Q. Xu.


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Tuesday, May 3, 2004, 4:00 p.m., VV B113
Mattias Jonsson (University of Michigan, Ann Arbor)
 Attenuation of singularities of currents in dimension 2

Abstract: It is a classical result that a (singular) curve C defined
near the origin in C^2 can be desingularized: there exists a composition
of point blowups such that the total transform of C has simple normal
crossings. Generalizing recent work by Mimouni we show a version of
the result for an arbitrary positive closed current T defined near
the origin in C^2. Namely, there exists a composition of blowups such that
the total transform of T decomposes into the sum of a simple
normal crossings divisor and a positive closed current with arbitrarily
small Lelong numbers everywhere. Joint work with Charles Favre
at CNRS, Paris.