Friday, September 18, 2015 3:30 pm
-
3:30 pm
EDT (GMT -04:00)
Title: Hodge Theory on Matroids
| Speaker: | Eric Katz |
| Affiliation: | University of Waterloo |
| Room: | MC 5501 |
Abstract:
The
chromatic
polynomial
of
a
graph
counts
its
proper
colourings.
This
polynomial's
coefficients
were
conjectured
to
form
a
unimodal
sequence
by
Read
in
1968.
This
conjecture
was
extended
by
Rota
in
his
1970
address
to
assert
the
log-concavity
of
the
characteristic
polynomial
of
matroids
which
are
the
common
generalizations
of
graphs
and
linear
subspaces.
We
discuss
the
resolution
of
this
conjecture
which
is
joint
work
with
Karim
Adiprasito
and
June
Huh.
The
solution
draws
on
ideas
from
the
theory
of
algebraic
varieties,
specifically
Hodge
theory,
showing
how
a
question
about
graph
theory
leads
to
a
solution
involving
Grothendieck's
standard
conjectures.