関西作用素環セミナー

Kansai Operator Algebra Seminar


日時:2015年12月12日(土)--13日(日)

場所:城崎地区公民館(会議室)

     〒669-6195 兵庫県豊岡市城崎町桃島1057-1

    つちや(宿泊場所)

     〒669-6101 兵庫県豊岡市城崎町湯島573

アクセス:京都駅 11:25発 --- 特急きのさき5号 --- 13:49着 城崎温泉駅

      大阪駅 11:11発 --- 特急こうのとり7号 --- 11:43着 福知山駅 11:45 発 --- 特急きのさき5号 --- 13:49 着 城崎温泉駅

      大阪駅 9:20発 (新大阪駅 9:30発) --- 全但バス --- 12:41着 城崎温泉駅

プログラム


12月12日(土)
14:30〜15:30 David E Evans

Cardiff Univ.
K-theoretic approach to modular invariance in Conformal Field Theory and Subfactors.

I will describe recent work with Terry Gannon on the realisation of modular invariants for twisted doubles of finite groups through bivariant Kasparov theory.
15:45〜16:45 Thierry Giordano
 
Univ. of Ottawa
Approximate transitivity: an overview of this notion introduced by A. Connes and E.J. Woods

In 1981, A. Connes and E.J. Woods introduced the definition of an approximate transitive (AT) action of a group $G$ to characterize the flow of weights of the Araki- Woods factors of type III. A few years later they proved that the Poisson boundary of a (time dependent) random walk on $G$ is an amenable and AT space. In this talk, I will review the notion of approximate transitivity and present some new developments.
18:30〜21:00 懇親会
 

 

12月13日(日)
9:30〜10:30 Hun Hee Lee

Seoul National Univ.
Similarity degree of Fourier algebras

Pisier introduced the concept of similarity degree to attack the problem of Dixmier's similarity problem and Kadison's similarity problem in the same context. In this talk we will explain Pisier's similarity degree for completely contractive Banach algebras and apply to the case of Fourier algebra $A(G)$. We will show that for infinite QSIN groups (containing amenable or discrete groups) the similarity degree of the corresponding Fourier algebra is exactly 2. As a consequence we prove the following Fourier algebra version of Dixmier's similarity problem: any cb-homomorphism from $A(G)$ to $B(H)$ is similar to $*$-representation.
10:45〜11:45 松本 健吾
 
上越教育大
Full groups of Cuntz-Krieger algebras and Higman-Thompson groups (joint work with Hiroki Matui)

In 1960's, R. J. Thompson has initiated a study of finitely presented simple infinite groups. He has discovered first two such groups written $V_2$ and $T_2$. G. Higman has generalized the group $V_2$ to infinite family of finitely presented infinite groups. One of such family is the groups written $V_N, 2\leq N \in {\mathbb{N}}$ which are called the Higman-Thompson groups. They are finitely presented and their commutator subgroups are simple. In this talk, we generalize the Higman-Thompson groups $V_N, 2\leq N \in {\mathbb{N}}$ by using the continuous full groups $\Gamma_A$ of a one-sided topological Markov shift $(X_A,\sigma_A)$ for an irreducible matrix $A$ with entries in $\{0,1\}$. They are realized as equivalence classes of unitary groups of normalizers of the Cuntz-Krieger algebras with its canonical MASA. The isomorphism class of the group $\Gamma_A$ determines the continuous orbit equivalence class of the one-sided topological Markov shift $(X_A,\sigma_A)$, the isomorphism class of the Cuntz-Krieger algebra ${\mathcal{O}}_A$ and $\det(1-A)$. We will show that the group $\Gamma_A$ can be represented as a group $\Gamma_A^{\operatorname{tab}}$ of matrices, called $A$-adic tables, with entries in admissible words of the shift space $X_A$, and a group $\Gamma_A^{\operatorname{PL}}$ of right continuous piecewise linear functions, called $A$-adic PL functions, on $[0,1]$ with finite singularities. I will also talk about some related topics.

参加者名簿(2015/11/12更新)

  1. David Evans
  2. Thierry Giordano
  3. Hun Hee Lee
  4. 松本健吾
  5. 長田まりゑ
  6. 縄田紀夫
  7. 河東泰之
  8. 林倫弘
  9. Benoit Collins
  10. 河上哲
  11. 片山良一
  12. 山中聡恵
  13. 湯浅久利
  14. 小澤登高
  15. 戸松玲治
  16. 岡安類