Sep. 02 (Fri)
Caution! |
3:00 - 4:30 RIMS 110 |
Sriwulan Adji (Univesiti Sains Malaysia)
The partial-isometric crossed products of systems by semigroups of endomorphisms
The partial-isometric crossed product is the $\mathrm{C}^*$-algebra
constructed from the system in which the endomorphisms are
implemented covariantly by partial isometries. This class of
$\mathrm{C}^*$-algebras provides a good example of the Toeplitz algebras
${\mathcal T}_X$ associated to a product system of Hilbert bimodules $X$
over a semigroup, which was introduced by Fowler (2002). I am interested
in particularly getting a description about invariant ideals of the
crossed product.
In this talk, I will first discuss about some basic known results
from the paper of Lindiarni and Raeburn. Then I will explain some
various connections to the isometric crossed products and hence to
the usual crossed product by groups of automorphisms.
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Sep. 02 (Fri)
Caution! |
4:45 - 6:15 RIMS 110 |
Ilan Hirshberg (Ben Gurion University)
Rokhlin dimension for automorphisms of $\mathrm{C}^*$-algebras
I will discuss a generalization of the Rokhlin property for an
automorphism, which can be thought of as a higher dimensional analogue.
This property is more common than the Rokhlin property, and
is still strong enough to establish permanence properties for finite
nuclear dimension and ${\mathcal Z}$-stability.
This is joint work with Wilhelm Winter and Joachim Zacharias.
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Sep. 05 - 09 |
RIMS |
Conference on $\mathrm{C}^*$-Algebras and Related Topics |
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Oct. 05 | 2:45 - 4:15 RIMS 006 |
Chris Phillips (University of Oregon/RIMS)
Equivariant semiprojectivity
Semiprojectivity of a $\mathrm{C}^*$-algebra $A$ is the most useful formulation of
the idea that approximate homomorphisms from $A$ should be close to exact
homomorphisms. For example, the algebra of continuous functions on the
circle is semiprojective, essentially because an approximate
homomorphism to $B$ corresponds to an approximately unitary element in $B$,
and the nearby exact homomorphism comes from the unitary part of its
polar decomposition.
We investigate a version of semiprojectivity which requires equivariance
with respect to an action of a compact group. Unconventional methods
seem to be required. A number of open problems will be stated. The talk
should be accessible without background in the area.
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Oct. 12 |
2:45 - 4:15 RIMS 006 |
Narutaka Ozawa (RIMS)
On Simple Finitely Generated Amenable Groups (after Grigorchuk and Medynets)
Grigorchuk and Medynets discovered the first examples of infinite finitely generated
groups that are simple and amenable. More precisely, they proved that the topological
full groups of any minimal transformation on the Cantor space is amenable.
It was previously known that the commutator subgroup of such a group is simple
(Bezuglyi--Medynets and Matui) and sometimes finitely generated (Matui).
I will discuss these results and their background.
arXiv:1105.0719
NB: There is a flaw in the proof of Lemma 4.4 (v2).
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Oct. 12 Colloquium |
4:30 - 5:30 MATH 110 |
Benoît Collins (University of Ottawa/RIMS)
New results in Free Probability theory and applications to Quantum Information theory
Motivated by Operator Algebraic questions, Voiculescu introduced Free
Probability in the early eighties. Ten years later, he discovered that
Free Probability explains some behaviours of eigenvalues of Random
Matrices in the limit of large dimension.
In this talk we will first describe new convergence results for norms
for random matrices with unitary invariance, hereby solving
conjectures by Pisier and Haagerup. Then, we will describe some
applications to Quantum Information theory.
This talk is based on results obtained through collaborations with
Belinschi, Nechita, Fukuda and Male.
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Oct. 19 |
2:45 - 4:15 RIMS 006 |
Chris Phillips (University of Oregon/RIMS)
Analogs of Cuntz algebras on $L^p$ spaces
The Cuntz algebras are among the most important examples of $\mathrm{C}^*$-algebras.
The algebra ${\mathcal O}_d$ is generated by $d$ isometries on a Hilbert space with
orthogonal ranges which add up to the whole space, and their adjoints.
It does not depend on the choice of the isometries.
It turns out that for $p > 1$ and finite, there is a very similar
statement in which the Hilbert space is replaced by $L^p (X)$. The
resulting algebras are purely infinite and simple, and have the same
K-theory as the usual Cuntz algebras. For different values of $p$ they
are strongly incomparable: there is no nonzero continuous homomorphism
from one to the other.
The subject is just getting started: so far, there is little complicated
machinery, and there are many open questions.
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Oct. 25 - 28 |
ShuGakuIn |
Operator Algebras and Mathematical Physics
at Kansai Seminar House
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Nov. 02 |
Okinawa
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No Talk
(Annual Workshop on Operator Theory and Opretaor Algebras, Ryukyu University, Nov. 03-06.)
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Nov. 08 (Tue)
Caution! |
1:15 - 2:45 RIMS 110 |
Étienne Blanchard (Institut de Mathématiques de Jussieu)
Fiberwise products of $\mathrm{C}^*$-bundles
We describe which classical amalgamated products of continuous $\mathrm{C}^*$-bundles are continuous $\mathrm{C}^*$-bundles and we analyse the involved extension problems for continuous $\mathrm{C}^*$-bundles.
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Nov. 16 |
2:45 - 4:15 RIMS 006 |
Yoshikata Kida (Kyoto University)
Invariants for orbit equivalence relations of Baumslag-Solitar groups
For non-zero integers $p, q$, the Baumslag-Solitar group $\mathrm{BS}(p,q)$
is defined by the presentation $\langle a, t \mid ta^pt^{-1}=a^q\rangle$.
We consider ergodic free probability-measure-preserving actions of $\mathrm{BS}(p,q)$,
and introduce an invariant of them under orbit equivalence.
We also present results on groups which are measure equivalent to $\mathrm{BS}(p,q)$.
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Nov. 23 |
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Holiday (Labor Thanksgiving Day) |
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Nov. 30 |
2:45 - 4:15 RIMS 006 |
Masaki Izumi (Kyoto University)
A weak homotopy equivalence type result related to Kirchberg algebras
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Dec. 06 (Tue)
Caution! |
2:45 - 4:15 RIMS 111 |
Snigdhayan Mahanta (University of Adelaide)
On the integral algebraic K-theoretic Novikov conjecture
The Novikov conjecture in topology is known to follow from the (rational) injectivity of the Baum-Connes assembly map. For a discrete and torsion free group $G$ the integral algebraic K-theoretic Novikov conjecture asserts the (split) injectivity of a similar Loday assembly map. After recalling briefly some background material, in this talk I shall show how any countable discrete and torsion free subgroup of a general linear group over any field satisfies the integral algebraic K-theoretic Novikov conjecture with coefficients in certain operator algebras.
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Dec. 07 - 16 |
RIMS |
Winter School on Operator Algebras
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Dec. 12 - 16 |
RIMS |
Analysis and Geometry of Discrete Groups and Hyperbolic Spaces
(Program in Japanese)
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Dec. 17 - 18 |
Kinosaki |
Kansai Operator Algebra Seminar
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Dec. 19 - 21 |
RIMS |
Mathematical Studies on Independence and Dependence Structure
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Winter Break | |
BouNenKai (Forget Year Party): Dec. 21 |
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Jan. 09 - 13 |
RIMS |
Conference on von Neumann Algebras and Related Topics
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Jan. 11 Colloquium |
4:30 - 5:30 RIMS 110 |
Chris Phillips (University of Oregon/RIMS)
Existence of outer automorphisms of the Calkin algebra is undecidable
Let $H$ be a separable infinite dimensional Hilbert space,
for example, the space $\ell^2$ of all square summable sequences.
Let $L (H)$ be the algebra of all continuous linear maps from
$H$ to $H,$ and let $K (H)$ be the closure in $L (H)$ of the set
of continuous linear maps which have finite rank.
Then $K (H)$ is an ideal in $L (H),$ and we can form the quotient
algebra $Q = L (H) / K (H)$.
It is called the Calkin algebra, and is an example of a $\mathrm{C}^*$-algebra.
Question: Does the Calkin algebra have outer automorphisms, that is,
automorphisms not of the form $a \mapsto u a u^{-1}$ for suitable
$u \in Q$ ?
It turns out that this question is undecidable in ZFC.
If one assumes the Continuum Hypothesis, then outer automorphisms exist.
In fact, there are more automorphisms than there are possible choices
for $u$. (This is joint work with Nik Weaver.)
However, Ilijas Farah proved that it is consistent with ZFC that
$Q$ has no outer automorphisms.
This talk is intended for a general audience.
I will describe some of the background, and give several of the
ideas of the proof that the Continuum Hypothesis implies the
existence of outer automorphisms of the Calkin algebra.
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Jan. 18 |
2:45 - 4:15 RIMS 006 |
Volodymyr Nekrashevych (Texas A&M University)
$\mathrm{C}^*$-algebras of hyperbolic groupoids
Hyperbolic groupoids is a generalization of such notions as Gromov hyperbolic group actions on their boundaries, groupoids generated by expanding maps, Ruelle groupoids of Smale spaces, etc. An interesting aspect of the theory of hyperbolic groupoids is a duality theory: rather than a groupoid acting on its boundary, we get a pair of groupoids acting on each others boundaries. We will discuss $\mathrm{C}^*$-algebras associated with hyperbolic groupoids (e.g., with hyperbolic complex rational functions), the corresponding duality theory, and applications to dynamics.
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Feb. 22 Colloquium |
4:30 - 5:30 MATH 110 |
Narutaka Ozawa (RIMS)
Is an irng singly generated as an ideal?
I will address the problem whether every finitely generated idempotent
ideal of a ring is singly generated as an ideal, and discuss its relationship
to the Wiegold problem. Joint work with N. Monod and A. Thom.
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Spring Break | |
Semester End |
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