OVERVIEW
FROM OUR PROPOSAL:
Graph C*-algebras have played a very important role in operator
algebra during the last 20 years. During the past 10 years, the subject
has blossomed substantially. Graph algebras and the technology surrounding
them appear in almost every aspect of operator algebra. They are an
extremely rich source of examples and they turn out to be fundamental
examples of operator algebras of current intense interest. There have been
a number of develpments in the theory, many of them the product of the
efforts of the proposed principal lecturer, Professor Iain Raeburn, that
lead one to conclude that it is timely to have a synopsis of the subject
to this point. This would help anchor future research in the theory and in
the applications of graph algebras to a variety of diverse subareas of
operator algebra.
Graph algebras are especially well-suited to help expose young
mathematicians to problems of current interest in the
study of operator algebras. The initial ideas involved in the study of
these algebras are quite easy to understand and the algebras are easily
manipulated. The "cost of admission" to operator algebras through graph
algebras is really quite low. The lectures are intended to be particularly
accessible to graduate students with limited backgrounds and to others who
know no more than the rudiments of C*-algebra theory. Thus, it is
expected that the lectures, the conference surrounding them, and the
subsequent monograph will contribute substantially to bringing young
mathematicians into contact with current active frontiers in mathematics.
The hope is that this will considerably expand the pipeline of
mathematicians.
USEFUL BACKGROUND FOR STUDENTS: The subject matter of this
conference is the interaction between discrete mathematical structures,
particularly directed graphs, and the theory of operator algebras. The
lecturer will assume that the participants are familiar with elementary
functional analysis, and in particular with the basic theory of Hilbert
space
and bounded operators. He will also assume familiarity with the rudiments
of C*-algebras: almost any course on C*-algebras which goes as far as
positivity, ideals and quotients should suffice. Many of the other topics
which are often taught in parallel with these ones, such as
Lebesgue integration and von Neumann algebras, will not be needed here. No
previous acquaintance with directed graphs or other aspects of
combinatorics
will be assumed.
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