Linear Analysis Seminar

Date Time 
Location  Speaker 
Title – click for abstract 

01/30 2:00pm 
BLOC 220 
Dave Penneys Ohio State 
Standard invariants for discrete subfactors
The standard invariant of a finite index II_1 subfactor is a
$\lambda$lattice and forms a planar algebra. In turn, the planar
algebra formalism has been helpful in constructing and classifying
subfactors, as well as studying analytic properties. In joint work
with Corey Jones, we give a wellbehaved notion of the standard
invariant of an extremal irreducible discrete subfactor $N\subset M$,
where $N$ is type II_1 and $M$ is an arbitrary factor. We also get a
subfactor reconstruction theorem. This generalizes the standard
invariant for finite index subfactors to a natural class of infinite
index subfactors. Particular examples include the symmetric enveloping
inclusion and examples coming from discrete quantum groups.


02/09 4:00pm 
BLOC 220 
Mateusz Wasilewski IMPAN 
Nonconjugacy of generator MASAs in qGaussian algebras
In the study of group von Neumann algebras, sometimes maximal abelian subgroups give rise to maximal abelian subalgebras (MASAs); it happens so for free groups and abelian subgroups generated by a single free generator. These subalgebras are conjugate by an automorphism (coming from the automorphism of a free group), but not by an inner automorphism. Free group factors also admit a different representation, using Voiculescu's free Gaussian functor; in this setting one can generate a MASA using a vector from a real Hilbert space. Bożejko and Speicher introduced a deformation of free group factor, called the qGaussian algebras for which analogues of generator MASAs can be defined. I will show that these MASAs are never conjugate by an inner automorphism, using Popa's intertwining techniques (joint work with Martijn Caspers and Adam Skalski).


03/09 4:00pm 
BLOC 220 
Alexandru Chirvasitu University at Buffalo 
Most metric spaces are very asymmetric
Compact quantum groups are the noncommutative geometer's version of a
compact group, and their actions on geometric or algebraic objects
capture extended notions of symmetry, generalizing the concept of a
structurepreserving automorphism.
The talk will explain what it means for a compact quantum group action
on a compact metric measure space to preserve the entirety of the
structure (metric as well as measuretheoretic). The main result is
then a reflection of the general intuition that most objects are not
very symmetric: upon topologizing the set of isomorphism classes of
metric measure spaces it transpires that ``the majority'' admit no
symmetry, even when relaxing the notion of symmetry to allow for its
quantum counterpart.
(partly joint w/ Martino Lupini, Laura Mancinska and David Roberson)


03/26 2:00pm 
BLOC 628 
Pierre Tarrago CIMAT 
Subordination methods for free deconvolution
The classical deconvolution of measures is an important problem which consists
in recovering the distribution of a random variable from the knowledge of
the random variable modified by an independent noise with known distribution.
In this talk, I will discuss the free version of this problem: how can we recover
the distribution of a noncommutative random variable from the knowledge of
the distribution of the random variable modified by the addition (or multiplication)
of a free independent noise ? Since large independent random matrices
in general positions are approximately free, an answer to the former question is
a first step in the extraction of the spectral distribution of a large matrix from
the knowledge of the matrix with an additive or multiplicative noise.
Contrary to the classical case, the free convolution is not described by an
integral kernel like the Fourier transform. This problem has been circumvented
by Biane, Voiculescu, Belinschi and Bercovici which developed a fixed point
method called subordination. I will explain how this method can be used to
reduce the free deconvolution problem to a classical one. This is a joint work
with Octavio Arizmendi (CIMAT) and Carlos Vargas (CIMAT). 

04/07 4:00pm 
BLOC 220 
Dmitriy Zanin University of New South Wales 
TBA
TBA 

04/13 4:00pm 
BLOC 220 
Jurij Volcic BenGurion University of the Negev 
TBA
TBA 
Archives
2008
•
2007
•
Prior to 2007
The organizer for this seminar is
David Kerr.