# What is a free group factor

### Prof. Dr. Roland memory

### Jun.-Prof. Dr. Moritz Weber

### Seminar / advanced seminar

to operator algebras and free probability theory

(Summer semester 2015)### Current

**Another room change: The seminar is now taking place in SR 2!**

### time and place

Mon 10-12, SR 2 (E2 5)- Monday, April 20 --- no meeting
- Monday, April 27 Pascal
*Lecture Gelfandt theory* - Monday, 4.5. Simon
*Lecture C * -Algebras* - Monday, May 11th --- no meeting
- Monday, May 18 Meeting to discuss the first reading
*Gelfandt theory and C * algebras* - Monday, May 25 --- no meeting
- Monday, 1.6. Felix
*Lecture Von Neumann Algebras* - Monday, 8th June --- no meeting
- Monday, June 15 Meeting to discuss the second reading
*Von Neumann algebras* - Monday, June 22nd Marvin
*Lecture Free Probability Theory* - Monday, June 29th --- no meeting
- Monday, 6.7. --- Meeting to discuss the third reading
*Free probability theory* - Monday, July 13th --- no meeting
- Monday, July 20 --- Meeting to discuss the fourth reading
*Free probability theory* - Monday, July 27 --- no meeting

### content

In order to study operators on the Hilbert space it is often helpful not only to consider individual operators,but the algebras they generate, provided with a topological closure. The study of such

Operator algebras provide e.g. the functional calculus, one of the most powerful tools in functional analysis.

In addition, some methods and thought patterns from algebra can also be developed for operators on Hilbert spaces

become. In a way it is the study of algebras of (complex valued) functions that do not commute,

so where

*fg = gf*for functions

*f*and

*G*is no longer fulfilled. Such mathematics is used, among other things, for quantum mechanics

needed, but also for some novel concepts of non-commutative geometry or non-commutative analysis.

Following on from the functional analysis, we will develop the basics of Gelfandt theory and GNS construction,

*C **- Define and Von Neumann algebras and study their basic properties and finally in a

current and very active research area immersing free probability theory. The latter is historically off

a still (for more than 70 years) open problem about Von Neumann algebras arose (the free

Group factor problem), but has now become an independent mathematical subject with relationships

developed for functional analysis, combinatorics, function theory, random matrices and much more. We will

Choose operator-algebraic approach and treat the basic concepts of freeness and non-commutative distributions.

Bachelor or master theses can be awarded after the seminar.

Announcement of the seminar

### literature

Jacques Dixmier,*Les C * -algebres et leurs representations*, 1969.

Gerard Murphy,

*C * algebras and operator theory*, 1990.

Bruce Blackadar,

*Operator algebras. Theory of C * -algebras and von Neumann algebras*, 2006.

Kenneth Davidson,

*C * algebras by example*, 1996.

Alexandru Nica and Roland Speicher,

*Lectures on the Combinatorics of Free Probability*, 2006 (call number Bibl. Inf + Math: LMS 335).

If you have any further questions, please contact Moritz Webermelden!

- Where's Jho Low
- Why was Barney Friends canceled
- How similar are Bulgarian and Serbian languages
- Is the relativistic mass out of date
- What are some common craigslist scams
- What is the relationship between gravity and time
- How do you make money blogging
- Describe the music theory in three words
- How are US states provided with numbers
- Which profession should I prefer after graduation?

- How do I rate a share
- Kurdish is an Iranian language
- But nobody noticed what has disappeared
- Which is habitable Titan or Mars
- What do you know about solar panels
- Why are odd numbers odd
- Who does photo shoots for beginners fashion bloggers
- How would you choose your death
- Where is the Mumbai High Oilfield
- How is it in the Navy
- Why do intelligent people reproduce less?
- What happens when the Antarctic melts
- Where are caldera volcanoes found
- You can use Kodi without internet
- Did Kumar Vishwas leave the Aam Aadmi party
- How intelligent is Warren Buffett
- Can Russian women marry Chinese men
- Does loneliness correspond to a higher IQ
- What's killing your Quora experience
- What is the hardest handmade thing to sell
- Is 0 2 greater than 0 05
- Who killed Crassus
- Was Draco Malfoy a Death Eater
- Do you really believe in the Bible?