Reading Seminar on Free Probability Theory
Lecturer: Roland Speicher
Assistant: Felix Leid
- The weekly meeting will take place on Wednesdays, 16 c.t. in Seminarraum 10, E2 4. First meeting is on April 20.
- If you are interested in participating, please write an email to Roland Speicher (firstname.lastname@example.org).
- This reading seminar is intended to give an introduction to the subject of free probability theory. We will rely on 26 lectures on this topic which were recorded a few years ago and on the corresponding lecture notes.
- We will meet once a week and discuss the material corresponding roughly to two of the recorded lectures.
- In addition there are also two books of the lecturer on free probability which can also be used for background information:
- A. Nica and R. Speicher: Lectures on the Combinatorics of Free Probability Theory
- J. Mingo and R. Speicher: Free Probability and Random Matrices
- more literature on the subject
- By successful participation students can acquire 4.5 credit points.
- To get credit for the class one has to participate in the regular meetings and to give at the end of the term one talk on a topic in the context of free probability.
- There is the possibility to set up topics for bachelor and master theses based on the class.
Free probability is a quite young mathematical theory with many avatars. It started in the theory of operator algebras, showed its beautiful combinatorial structure via non-crossing partitions, made contact with the world of random matrices, and reached out to many other subjects like representation theory of large groups, quantum groups, invariant subspace problem, large deviations, quantum information theory, subfactors, or statistical inference. Even in physics and engineering, people have heard of it and find it useful and exciting.
This Reading seminar is in a sense a continuation of classes on Random Matrices and on Operator Algebras, as it deals with the concept of freeness or free independence, which appears both in the limit of random matrices as well as for important classes of von Neumann algebras. On the other hand, freeness is an important concept for its own sake which deserves to be investigated independently of its random matrix or operator algebraic roots. That's what we will do in this class; we will, in particular, look at the combinatorial, analytical and probabilistic structure of freeness.
Its relations to random matrices and to operator algebras (and in particular its use in those contexts) will also be covered, however, depending on the audience, we will recall the relevant basic knowledge from those subjects; i.e., having taken an operator algebra and/or random matrix course is surely helpful, but not required for this class.
Department of Mathematics
Postfach 15 11 50
Campus building E 2 4