Seminar on Free Probability
and Random Matrices

Fall 2018

Organizer: J. Mingo


Thursday, October 18, 4:30 - 6:00, Jeff 422
Pei-Lun Tseng (Queen's)
Right Hilbert A-modules, part 2
For the last talk, we gave some motivating examples and the definition of right A-module. We will begin this talk by showing some properties of  A-valued pre inner product, and then we will deduce the process to construct a right Hilbert A-module. Next, we will introduce the operators on  right Hilbert A-modules, and proving some properties of the corresponding adjoint operators. 
Thursday, October 11, 4:30 - 6:00, Jeff 422
Pei-Lun Tseng (Queen's)
Right Hilbert A-modules
Last week, we gave a sketch of proving the GNS construction. We will start to introduce the matrices over a C*-algebra this week, which is an application of the GNS construction. Then, we will begin the new topic: Right Hilbert A-modules. We will deduce the process to construct the inner product on a right Hilbert A-module H. As long as we have the inner product, we can consider the orthogonality on H and compare the different between the scalar case and $A$-valued case..
Thursday, October 4, 4:30 - 6:00, Jeff 422
Pei-Lun Tseng (Queen's)
$A$-Valued Theory
In order to study operator-valued probability, we need some basic knowledge of C*-algebras. In this talk, I am trying to review what is a C*-algebra.  and some properties of C*-algebras. The GNS construction will be covered, which is known as the follows: every C*-algebras can be represented as a algebra of bounded linear operators on a Hilbert space. This construction gives us good starting point to study matrices over a C*-algebra. If time permits, I will introduce right Hilbert $A$-modules.
Thursday, September 27, 4:30 - 6:00, Jeff 422
Jamie Mingo (Queen's)
Operator Values Freeness and Non-commutative functions, II
Free Additive Convolution and Subordination
Last week I reviewed the basic facts of scalar free independence. This week I will continue with a new convolution of probability measures called the free additive convolution. We will use a tool from complex analysis called subordination to get our convolution. It will then lead to a discussion of conditional expectation which will be the basis of operator valued freeness.
Thursday, September 20, 4:30 - 6:00, Jeff 422
Jamie Mingo (Queen's)
Operator Values Freeness and Non-commutative functions
This fall the seminar will be a learning seminar with lectures by (willing) participants. The theme will be operator valued freeness. This is the non-commutative version of conditional independence, now we have independence over a subalgebra. In many cases the subalgebras are n x n matrices so this is quite a general situation. I will begin by reviewing the basic facts of scalar free independence. The seminar will follow a recent book by D. Kaliuzhnyi-Verbovetskyi and V. Vinnikov and some lecture notes of D. Jekel.

Previous Schedules

Winter 2018
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Getting to Jeffery Hall from the Hotel Belvedere