Simon Marshall, Northwestern University
"L^p norms of eigenfunctions on locally symmetric spaces"
Let
M
be
a
compact
Riemannian
manifold,
and
f
an
L^2-normalised
Laplace
eigenfunction
on
M.
If
p
>
2,
a
theorem
of
Sogge
tells
us
how
large
the
L^p
norm
of
f
can
be
in
terms
of
its
Laplace
eigenvalue.
For
instance,
when
p
is
infinity
this
is
asking
how
large
the
peaks
of
f
can
be.
I
will
present
an
analogue
of
Sogge's
theorem
for
eigenfunctions
of
the
full
ring
of
invariant
differential
operators
on
a
locally
symmetric
space,
and
discuss
some
links
between
this
result
and
number
theory.
Refreshments will be served in MC 5046 at 3:30 pm. Everyone is welcome to attend.