作用素環論研究者シンポジウム
作用素環論の最近の進展 (Recent Developments in Operator Algebras)
２０２１年９月２７日(月) & ２８日(火)
Past Records:
2020
2019
2018
2017
2016
2015
2014
2013
Due to Covid19, this meeting will take place online via Zoom.
For the Zoom link, please answer the following question and show you are relevant.
Who wrote the celebrated Ring tetralogy?
Sept. 2021 
Monday, 27 
Tuesday, 28 
09:30  10:30 
Welcome
Program in pdf 

11:00  12:00 


Lunch 
13:30  14:30 


15:00  16:00 


A biunitary connection in subfactor theory producing a subfactor of finite depth gives a 4tensor appearing in a recent work on 2dimensional topological order and anyons. Physicists have a special finite dimensional projection called a "projector matrix product operator" in this setting. We prove that the range of this projection of length k is naturally identified with the kth higher relative commutant of the subfactor arising from the biunitary connection. This gives a further connection between 2dimensional topological order and subfactor theory.
We classify outer actions (or $\mathscr{G}$kernels) of discrete amenable groupoids on injective factors. Our method based on unified approach for classification of discrete amenable groups actions, and cohomology reduction theorem of discrete amenable equivalence relations. We do not use KatayamaTakesaki type resolution group approach.
We give a necessary and sufficient condition for dtuple of unitary operators in a finite von Neumann algebras to be free Haar unitaries in terms of the norm of an operator involving the d unitary operators. We will discuss some motivations, related results and some aspects of the proof.
This talk is based on the joint work with Leonard Cadilhac
arXiv:2103.02944.
Freed and Hopkins conjectured that the deformation classes of nontopological invertible quantum field theories are classified by a generalized cohomology theory called the Anderson dual of bordism theories. Two of the main difficulty of this problem are the following. First, we do not have the axioms for QFT's. Second, the Anderson dual is defined in an abstract way. In this talk, I will explain our results (
arXiv:2106.09270) to give a new approach to this conjecture, in particular to overcome the second difficulty above. We construct a new, physically motivated model for the Anderson duals. This model is constructed so that it abstracts a certain property of invertible QFT's which physicists believe to hold in general. I will start from basic motivations for the classification problem, report the progress of our work and explain future directions.
This is the joint work with Kazuya Yonekura (Tohoku, physics).
The notion of sandwiched Rényi divergences (a oneparameter extension of the relative entropy) has played a role in quantum information, which has recently been generalized to the von Neumann algebra setting by BertaScholzTomamichel and Jenčová. In this talk we discuss properties of sandwiched Rényi divergences and their relation with the strong converse exponent (showing up in the strong converse type of quantum hypothesis testing), extending Mosonyi and Ogawa's result in the finitedimensional case to the von Neumann algebra case (also the C*algebra case).
The talk is based on ongoing work with Milán Mosonyi.
I would like to talk about bundles of the Cuntz algebras and their relationship to DadarlatPennig's cohomology groups. I will also explain a one to one correspondence between the sets of bundles whose fibers are the Cuntz algebra with n+1 generators and the tensor product of n by n matrix algebra and the infinite Cuntz algebra.