ì—p‘fŠÂ˜_‚̉č‡h (Summer Camp on Operator Algebras)
¬’M, 2014”N07ŒŽ19“ú - 22“ú Otaru (Hokkaido), July 19 - 22, 2014

Organizers: R. Okayasu, N. Ozawa (chief), and R. Tomatsu

  19 (Saturday) 20 (Sunday) 21 (Monday) 22 (Tuesday)
09:30   
- 11:30
 
 
Ozawa ‚P Ozawa ‚Q Ozawa ‚R
 
 
 
 
Lunch Break
14:30   
- 16:00
Suzuki Hiking Hasebe
 
16:30   
- 18:30
Houdayer ‚P Houdayer ‚Q Houdayer ‚R
 
–é
Evening
Problem Session
20:00-21:00
§e‰ï (Barbecue)
19:00-21:00
ƒ[ƒhƒ}ƒbƒv‰ï‹c
20:00-21:00

Cyril Houdayer: Structure of free product von Neumann algebras.

I will survey various recent results regarding the structure of free products of arbitrary von Neumann algebras.
Lecture 1: I will review several tools that are useful in the structure theory of von Neumann algebras. These include Cartan subalgebras, Popa's intertwining techniques, Connes-Takesaki's continuous decomposition and ultraproduct von Neumann algebras.
Lecture 2: I will outline the proof of a joint result with R. Boutonnet and S. Raum showing that free products of arbitrary von Neumann algebras have no Cartan subalgebra.
Lecture 3: I will outline the proof of a recent result showing that any diffuse amenable von Neumann algebra is maximal amenable inside its free product with an arbitrary von Neumann algebra.

Narutaka OzawaFNoncommutative Real Algebraic Geometry.

I will give an introduction to the emerging (?) subject of "noncommutative real algebraic geometry," a subject which deals with equations and inequalities in noncommutative algebras over the reals, with the help of analytic tools such as representation theory and operator algebras.

Takahiro Hasebe: Free independence and free cumulants

Free independence is the abstraction of relationship of generators of a free group. I would like to explain free cumulants which give us clear understanding of free independence.

Yuhei Suzuki: Some isomorphism theorems of O_2 (Theorem of Elliott and Rørdam)

The goal of this minilecture is to give a proof of Elliott--Rørdam's isomorphism theorem: \bigotimes _{n\in N}O_2 \cong O_2. The study of the endomorphism on the UHF-core of O_2 and that of homomorphisms on O_2 are the key of the proof.

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