Vasileos (Hector) Papoulias, Oxford University
"Spin(7) Instantons and HYM Connections on Asymptotically Conical Calabi-Yau Fourfolds"
The
Spin(7)
and
SU(4)
structures
on
a
Calabi-Yau
(CY)
fourfold
give
rise
to
certain
first
order
PDEs
defining
special
Yang-Mills
connections:
the
Spin(7)
instanton
equations
and
the
Hermitian
Yang-Mills
(HYM)
equations
respectively.
The
latter
are
stronger
than
the
former.
In
1998
C.
Lewis
proved
that
-over
a
compact
base-
the
existence
of
an
HYM
connection
implies
the
converse
establishing
equivalence.
In
this
talk
we
present
recent
progress
on
the
relationship
between
the
two
equation
systems
in
the
asymptotically
conical
(AC)
setting.
We
extend
Lewis’s
argument
under
assumptions
on
the
asymptotic
decay
rate
and
construct
a
counterexample
demonstrating
that
these
assumptions
cannot
be
relaxed.
In
doing
so,
we
construct
the
full
moduli
space
of
SO(5)
invariant
Spin(7)
instantons
over
the
Stenzel
manifold.
These
are
the
first
examples
of
pure
(non-HYM)
Spin(7)
instantons
coexisting
with
HYM
solutions
-
a
phenomenon
precluded
in
the
compact
world
by
Lewis's
original
argument.
This
paves
the
way
to
higher
resolution
questions
regarding
the
relationship
between
the
two
systems.
The
aforementioned
moduli
space
exhibits
a
curious
removable
singularity/
bubbling
phenomenon
that
might
prove
a
first
step
in
this
direction.
This seminar will be held jointly online and in person:
- Zoom link: https://zoom.us/j/93859138328; Passcode: 436044
- Room: MC 5417