Talk
#1:
(1:00pm-2:00pm)
Amanda
Petcu
"The
$G_2$
Laplacian
flow
and
Laplacian
solitons"
This
talk
will
introduce
the
$G_2$-Laplacian
flow
for
closed
$G_2$
structures
on
a
compact
manifold.
We
will
show
its
relationship
with
a
natural
volume
functional
and
discuss
the
main properties
of
the
flow
such
as
short-time
existence
and
the
evolution
of
the
induced
metric
and
volume
form.
Moreover,
we
will
introduce
the
soliton
solutions
of
the
Laplacian
flow,
proving
a non-existence
result
except
in
the
case
of
a
torsion-free
$G_2$
structure.
Talk
#2:
(2:15pm-3:45pm)
Spiro
Karigiannis
"The
deTurck
trick
demystified
(Part
II)"
This
is
a
continuation
of
last
week's
talk.
The
Ricci
flow
is
not
strictly
parabolic
due
to
diffeomorphism
invariance.
This
makes
it
harder
to
prove
short-time
existence
of
the
flow.
I
will
explain
the
“deTurck
trick”
to
break
the
diffeomorphism
invariance
(also
called
gauge-fixing).
This
produced
a
modified
flow
that
is
strictly
parabolic.
One
then
shows
that
a
solution
to
the
modified
flow
can
be
transformed
into
a
solution
of
the
original
flow.
MC
5403