Daniel Platt, King's College London
"A construction of associative submanifolds near the singular limit"
Associative
submanifolds
are
certain
3-dimensional
manifolds
in
7-dimensional
manifolds.
They
are
calibrated,
and
therefore
minimal
surfaces,
and
there
is
a
research
programme
that
attempts
to
count
them
in
order
to
define
numerical
invariants
of
manifolds,
similar
to
Gromov-Witten
invariants.
However,
not
many
examples
of
associative
submanifolds
are
known,
which
is
one
of
the
difficulties
in
working
out
the
details
of
this
programme.
In
the
talk
I
will
explain
how
to
construct
some
dozens
of
associatives
whose
existence
had
previously
been
predicted
by
physicists.
They
are
different
from
all
previously
known
associatives
in
that
their
volume
goes
to
zero
as
the
ambient
manifold
converges
to
a
certain
singular
limit.
This
is
joint
work
with
Shubham
Dwivedi
and
Thomas
Walpuski.
MC
5417