Thursday, **November 29**, 4:30 - 6:00, Jeff 422

Gang-Gyun Youn (Queen's)

Some questions on Jones-Wenzl projections in view of quantum
information theory

It is very natural to study separability or PPT property
of quantum states in view of quantum information theory and the need to
study those properties for so-called Jones-Wenzl projections has emerged in
recent years. In this talk, I am going to introduce the notions of
separability, PPT property and Jones-Wenzl projections.

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.

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