ì—p‘fŠÂ˜_‚Ì‰Ä‡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 20:0021:00 
§e‰ï (Barbecue) 19:0021:00 
ƒ[ƒhƒ}ƒbƒv‰ï‹c 20:0021:00 
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, ConnesTakesaki'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 OzawaFNoncommutative 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 ElliottRørdam's isomorphism theorem: \bigotimes _{n\in N}O_2 \cong O_2. The study of the endomorphism on the UHFcore of O_2 and that of homomorphisms on O_2 are the key of the proof.ŽQ‰Á—\’èŽÒ: ˆ¢•”áÁ‘¸, r–ì—I‹P, ’r“cN, ˆé–ì—D‰î, Cyril HOUDAYER, ‰ªˆÀ—Þ, ¬àV“o‚, —é–Ø—I•½, ›¸“cŸ©ˆê, •Î‘ñ–ç, ŒË¼—æŽ¡, ’·’JìŒd, ’·’J•”‚L, ‘£—F—T, ‘–{Žü•½, ŽR‰º^