| Date: | January 30, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 220 |
| Speaker: | Dave Penneys, Ohio State |
| Title: | Standard invariants for discrete subfactors |
| Abstract: | 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 well-behaved 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.
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| Date: | February 9, 2018 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | Mateusz Wasilewski, IMPAN |
| Title: | Non-conjugacy of generator MASAs in q-Gaussian algebras |
| Abstract: | 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 q-Gaussian 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).
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| Date: | March 9, 2018 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | Alexandru Chirvasitu, University at Buffalo |
| Title: | Most metric spaces are very asymmetric |
| Abstract: | Compact quantum groups are the non-commutative 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
structure-preserving 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 measure-theoretic). 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)
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|
| Date: | March 26, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Pierre Tarrago, CIMAT |
| Title: | Subordination methods for free deconvolution |
| Abstract: | 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 non-commutative 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). |
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| Date: | April 6, 2018 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | Dmitriy Zanin, University of New South Wales |
| Title: | Estimates on the singular values for generalised Hilbert transform and double operator integrals |
| Abstract: | If $Hf$ is a Hilbert transform of a function $f,$ then it is well known that $\mu(Hf)\leq (C+C^*)\mu(f),$ where $C$ is the Cesaro operator. This estimate is the best possible.
This talk aims to provide a noncommutative analogue of this classical result. The following is demonstrated: if an operator $T$ satisfies $\mathcal{L}_1\to\mathcal{L}_{1,\infty}$ estimate, then $\mu(T(A))\leq (C+C^*)\mu(A).$
In particular, the latter estimate applies to triangular truncation operator (which is considered a noncommutative version of a Hilbert transform). It also applies to certain types of double operator integrals. We show that the estimate above is the best possible for the triangular truncation operator." |
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| Date: | April 13, 2018 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | Jurij Volcic, Ben-Gurion University of the Negev |
| Title: | A Nullstellensatz for noncommutative polynomials: advances in determinantal representations |
|
| Date: | May 4, 2018 |
| Time: | 4:00pm |
| Location: | BLOC 220 |
| Speaker: | François Le Maître, Institut de Mathématiques de Jussieu–PRG Université Paris Di |
| Title: | Quasi-isometry of inverse limits of finite symmetric groups and derived L^1 full groups |
| Abstract: | In this talk, we will make sense of the following question: is the group of dyadic permutations quasi-isometric to the group of triadic permutations ?
We will see that this question is linked to some Polish groups which are called derived L^1 full groups of measure-preserving transformations, and that it can be reformulated as: are the derived L^1 full groups of the 2-odometer and of the 3-odometer quasi-isometric ? |
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