Talk #1 (9:30am - 10:30am): Anton Iliashenko, Department of Pure Mathematics, University of Waterloo
"Some results about Riemannian submersions"
We will go through some results about Riemannian submersions from the Arthur L. Besse's book on Einstein manifolds. For example, we will show that a surjective Riemannian submersion is harmonic iff the fibers are minimal, and some others as the time permits.
Talk #2 (10:45am - 12:15pm): Jean-Pierre Bourguignon, President, European Research Council
"What is a spinor?"
This
was
the
title
of
the
lecture
Sir
Michael
gave
in
September
2013
at
IHES
on
the
occasion
of
the
farewell
conference
for
my
retirement
as
Director.
This
was
most
appropriate
as
I
learned
a
lot
from
him about
this
subject.
It
is
true
that
mathematicians
struggled
for
a
long
time
to
get
acquainted
with
spinors.
It
is
in
sharp
contrast
with
the
fact
that
physicists
adopted
them
without
hesitation
as
soon
as
Paul-Adrien Maurice
Dirac
showed
they
were
essential
to
formulate
a
quantum
equation
invariant
under
the
Poincaré
group.
Indeed
spinors
have
a
number
of
features
that
make
them
both
subtle
and
powerful
to
deal
with mathematical
problems.
Of
great
importance
are
of
course
the
natural
differential
operators
universally
defined
on
spinor
fields,
namely
the
Dirac
and
the
Penrose
operators.
The
purpose
of
the
lecture
is
to
revisit historical
steps
taken
to
master
these
objects,
explore
their
remarkable
geometric
content
and
present
some
mathematical
problems
on
which
they
shed
light.
Note:
This
is
a
*pre-recorded
lecture*
which
was
given
as
part
of
the
Maxwell
Institute's
"Atiyah
Lecture
Series"
in
Edinburgh
on
January
11,
2021.
We
watched
the
first
half
of
the
lecture
two
weeks
ago,
and
we
will watch
the
rest
of
it
this
time.
As
we
did
last
time,
we
will
pause
the
video
at
any
moment
to
ask
each
other
questions
and
hopefully
get
meaningful
answers
from
each
other.
We
watched
the
first
half
in
Fall
2021,
but
never
finished
it,
and
there's
been
a
lot
of
turnover
in
our
audience,
so
we'll
just
watch
the
whole
talk
from
the
beginning.
The video is available here: https://www.icms.org.uk/events/2021/inaugural-atiyah-lecture-jean-pierre-bourguignon
MC 5403