The Rim Hook Rule: Relating Quantum Cohomology of the Grassmannian to Ordinary Cohomology of the Grassmannian
| Speaker: | Anna Bertiger |
|---|---|
| Affiliation: | University of Waterloo |
| Room: | Mathematics and Computer Building (MC) 5158 |
Abstract:
I
will
present
the
cohomology
ring
of
the
Grassmannian
of
k
planes
in
$\mathbb{C}^n$,
roughly
a
ring
with
generators
related
to
subspaces
of
the
Grassmannian
and
product
related
to
overlaps
up
to
translation.
It
turns
out
this
is
a
nice
polynomial
ring
with
many
combinatorial
properties.
The
same
is
true
of
the
quantum
cohomology
ring
of
the
Grassmannian,
which
has
the
same
generators
with
a
product
given
by
curves
joining
the
subspaces,
rather
than
overlap.
These
two
geometrically
motivated
rings,
which
seem
very
different
are
related
by
a
result
of
Bertram,
Ciocan-Fontanine
and
Fulton.
I
will
explain
this
result,
and
also
a
new
equivariant
version
of
this
result.
I
intend
for
the
talk
to
be
friendly,
with
all
of
the
geometric
notions
defined.
This
is
joint
work
with
Liz
Beazley
and
Kaisa
Taipale.