Ken Davidson, Department of Pure Mathematics, University of Waterloo.
The
Kadison-Singer
problem
is
a
long-standing
problem
in
operator
algebras
that
turns
out
to
be
equivalent
to
interesting
problems
in
frame
theory
and
harmonic
analysis.
It
was
recently
solved
using
probabalistic
matrix
theory
techniques
is
used
in
algebraic
graph
theory.
I
will
give
an
overview
of
the
problem
and
some
of
the
background
in
operator
algebras,
and
explain
some
of
the
equivalent
forms
including
the
one
which
is
verified
in
the
solution.
This
will
be
followed
in
subsequent
weeks
by
background
on
the
algebra
needed,
and
then
working
through
the
paper
"Interlacing
Families
II:
Mixed
Characteristic
Polynomials
and
the
Kadison-Singer
Problem"
by
A.
Marcus,
D.
Spielman
and
N.
Srivastava
arXiv:1306.3969
[math.CO].