"Word Measures on Groups"
Let
w
be
a
word
in
the
free
group
on
k
generators,
and
let
G
be
a
finite
(compact)
group.
The
word
w
induces
a
measure
on
G
by
substituting
the
letters
of
w
with
k
independent
uniformly
(respectively
Haar)
random
elements
of
G
and
evaluating
the
product.
I
will
explain
some
of
the
motivation
for
the
study
of
word
measures,
both
from
the
free
group
side
and
from
the
finite/compact
groups
side.
I
will
also
explain
some
properties
of
word-measure,
give
examples
and
state
conjectures.
As
much
as
time
permits,
I
will
describe
recent
results
regarding
word
measures
on
symmetric
groups
(joint
with
Ori
Parzanchevski)
and
word
measures
on
unitary
groups
(joint
with
Michael
Magee).
MC 5501
Refreshments will be served at 3:30pm in MC 5403. All are welcome!