This seminar treats anything related to operator algebras. Both research and survey talks are welcomed.

A list of talks before 2018 is available HERE(Professor Yamagami's website).

2019
Apr. 16 Ryosuke Sato (Nagoya)
Type classification of extremal quantized characters 
 The notion of quantized characters is introduced in our 
previous paper as a natural quantization of characters in the context of 
asymptotic representation theory for quantum groups. As in the case of 
ordinary groups, the representation associated with any extremal 
quantized character generates a von Neumann factor. In the viewpoint of 
operator algebras (and measurable dynamical systems), it is natural to 
ask what is the Murray-von Neumann-Connes type of the resulting factor. 
In this talk, we will give a complete solution to this question when the 
inductive system is of quantum unitary groups.


May 14 Amine Marrakchi (RIMS)
Tensor product decompositions and rigidity of full factors
A central theme in the theory of von Neumann algebras is to determine
all possible tensor product decompositions of a given factor.
I will present a recent joint work with Yusuke Isono where
we use the rigidity of full factors and a new flip automorphism
approach in order to study this problem. Among other things,
we show that a separable full factor admits at most countably
many tensor product decompositions (up to stable unitary conjugacy).
We also establish new primeness and Unique Prime Factorization results
for crossed products coming from compact actions of higher rank lattices
(e.g. SL_n(Z) for n > 2) as well as noncommutative Bernoulli shifts with arbitrary base (not necessarily amenable).


May 20--24 Christopher Jack Bourne (Intensive course, place and schedules)
An introduction to noncommutative geometry and some of its applications in index theory and mathematical physics




May 28 Yoshiki Aibara (Nagoya)
Self-polar form とその応用について(survey)
順序ベクトル空間上の特別なsesquilinear-formはself-polar formと呼ばれ、self-polar formがもつmaximum principle という性質は非自明な不等式を導く。
Haagerupは作用素環のself-polar formに注目することで部分代数に条件付き期待値が存在する条件を得た。
今回はself-polar formの基本的な性質やHaagerupの結果について紹介する。


Jun. 4 Yoshiki Aibara (Nagoya)
Self-polar form とその応用について II(survey)
(5/28の続き)


Jul. 2 Tomohiro Hayashi (Nagoya Institute of Technology)
On a norm inequality for a positive block-matrix. 

Let $A$, $B$ and $X$ be square matrices such that the block-matrix 
$H=
\begin{pmatrix}
A&X\\
X^{*}&B
\end{pmatrix}
$ 
is positive, or equivalently $B\geq X^*A^{-1}X$.
In this talk we investigate the norm inequality 
$||H||\leq ||A+B||$. 




Jul. 9 14:30-16:00!　Michiya Mori (Tokyo)
Order isomorphisms of von Neumann algebras
非負実数全体からそれ自身への順序同型は連続単調増加全単射に他なりません。
では、n 次半正定値行列全体からそれ自身への順序同型は何でしょうか。
実は、n が 2 以上であれば、このような写像は線形であることが知られています。
この事実を von Neumann 環の設定に一般化した結果、および、von Neumann 環
の一般の区間に対する順序同型についてお話しいたします。


Jul. 16 14:30-16:00!　Yuhei Suzuki (Nagoya)
Amenable actions on Kirchberg algebras and applications

私が二年前に発見した完全群のKirchberg環上の従順作用について復習した後，
これを用いたKirchberg環の接合積分解を紹介し，この分解表示がKirchberg環の従順でない興味深い現象を取り出すための
適切で強力な手段を与えることを，いくつかの応用を通して見ていきたいと思います．


Oct. 28 Taro Sogabe(Kyoto)
Cuntz-Toeplitz 環の自己同型群のホモトピー群について
Cuntz-Toeplitz環は互いに値域が直交するisometriesで生成される普遍的なC＊環であり、コンパクト作用素のなすC＊環とCuntz環の拡大として得られます。
M. Dadarlat氏によるCuntz環の自己同型群のホモトピー群の計算を踏まえて、Cuntz-Toeplitz環の自己同型群のホモトピー群の計算を紹介しようと思います。
またベクトル束からCuntz-Pimsner 環としてCuntz環のバンドルを作るM. Dadarlat 氏の仕事についても紹介しようと思います。



Nov. 5 (Tue) 14:00〜15:30 Masato Mimura(Tohoku)
LubotzkyとWeissの予想の極端な反例
1992年前後にLubotzkyとWeissは、コンパクト群の有限生成稠密部分群が従順群にもKazhdan群にもなり得るときは自明なとき
（つまり、コンパクト群が有限群のとき）以外ないのではないか、と予想した。
この予想は誤りである：2010年にErshovとJaikin-Zapirainによって反例が挙げられている。
本講演では、群のLEF（Locally Embeddable into Finite groups）近似を利用して、上の予想の「激しい反例」を構成する。

11/7，解析数論セミナー(15:00〜,　多元309号室)にて，同講演者の"Tao のスライスランク法と極値組合せ論"に関する講演があります．



Dec. 16 Keisuke Yoshida(Hokkaido)
Operator algebras from contracting self-similar group actions
自己相似群作用と呼ばれるカントール空間上の群作用からNekrashevychによって構成された作用素環について講演する．
今回は特にcontractingと呼ばれるある意味で有限生成性を課した自己相似群作用を取り扱う．
Contractingな自己相似群作用から構成されるCuntz--Pimsner環の上の自然なゲージ作用に対応するKMS状態が一意に存在することを示す．
またcontractingな自己相似群作用はグラフを用いて捉えることができることに触れ，
そのグラフが扱いやすい場合には唯一のKMS状態のGNS空間上のvon Neumann環が従順になることを示す．



Dec. 23 Shigeru Yamagami(Nagoya)
Spectral analysis of analytic functionals of geometric series
Inspired by Haagerup's positive definite functions on free groups,
we introduce certain polynomial hypergroups together with linear functionals of geometric series.
Their spectral analysis is then performed with help of Stieltjes inversion formula
to get a complete  description of the condition characterizing C*-functionals.



Jan. 6 Yosuke Kubota(RIKEN)
On some structural properties of self-similar groupoids
Self-similar action is a kind of group actions onto the regular rooted tree.
Nekrashevych defines an etale groupoid associated to a self-similar action,
which is a source of new interesting discrete groups as its topological full group.
According to Matui's theorem, isomorphism of the topological full groups is equivalent to that of the original groupoids.
In this talk, we introduce our approaches to distinguish the groupoids (and hence the associated topological full groups)
obtained from different self-similar actions. Key ingredients are groupoid homology and quasi-invariant measures on the object space. 
The talk is partially based on a joint work with Motoko Kato (Ehime Univ.).


Jan. 27 Yusuke Isono(RIMS)
Ergodic theory of affine isometric actions on Hilbert spaces
The classical Gaussian functor associates to every orthogonal representation of a locally compact group G
a probability measure preserving action of G called a Gaussian action.
We generalize this construction by associating to every affine isometric action of G on a Hilbert space,
a one-parameter family of nonsingular Gaussian actions whose ergodic properties are related
in a very subtle way to the geometry of the original action. We show that these nonsingular Gaussian actions exhibit
a phase transition phenomenon and we relate it to new quantitative invariants for affine isometric actions.
We use the Patterson-Sullivan theory as well as Lyons-Pemantle work on tree-indexed random walks in order to
give a precise description of this phase transition for affine isometric actions of groups acting on trees.
Finally, we use Gaussian actions to show that every nonamenable locally compact group without property (T) admits
a free nonamenable weakly mixing action of stable type III$_1$. This is joint work with Y. Arano and A. Marrakchi.



Feb. 12(Wed) 13:-00--14:30, Feb. 13(Thur) 15:30--17:00
Matthew Kennedy(University of Waterloo)
Noncommutative Choquet theory
I will present a new framework for noncommutative convexity and noncommutative function theory,
along with a corresponding noncommutative Choquet theory that generalizes much of classical Choquet theory.
I will also introduce a notion of noncommutative Choquet simplex, which generalizes the classical notion of
Choquet simplex and plays a similar role in noncommutative dynamics. I will discuss some applications,
including the following extension of Glasner and Weiss’s characterization of groups with Kazhdan’s property (T):
a group has property (T) if and only if whenever it acts on a C*-algebra,
the set of invariant states is affinely homeomorphic to the state space of a C*-algebra.


Feb. 17 Yusuke Sawada(Nagoya)
Hypergroups and random walks on graphs
 Wildbergerはグラフからその上のランダムウォークを用いて超群を得る方法を確立した。
超群とは群を確率論的に一般化した概念であり、*-環として記述される。
しかし、任意のグラフから超群が得られるわけではない。本講演では超群が得られるグラフの条件を解説し、
そのような条件下で、ランダムウォークの中の分布が超群の代数構造にどのように現れるかを解説する。