Friday, September 20, 2013 3:30 pm
-
4:30 pm
EDT (GMT -04:00)
Line arrangements and intersection theory on algebraic surfaces
| Speaker: | Eric Katz |
|---|---|
| Affiliation: | University of Waterloo |
| Room: | Mathematics and Computer Building (MC) 5158 |
Abstract:
Line
arrangements
in
the
plane
are
an
object
of
combinatorial
and
algebraic
geometric
interest.
Their
combinatorial
analogues
are
rank
3
matroids.
A
line
arrangement
determines
a
particular
algebraic
surface.
On
this
surface,
one
can
study
the
intersection
of
curves,
giving
an
intersection
theory
which
encodes
some
of
the
geometry
of
the
surface.
This
theory
can
be
immediately
extended
to
the
abstract
theory
of
rank
3
matroids.
This
gives
a
proof
of
the
unimodality
conjecture
in
this
case.
More
significantly,
it
gives
constraints
on
the
structure
of
the
Hasse
diagram
of
the
flat
poset
of
the
matroids
making
a
connection
with
algebraic
graph
theory.
This
work
is
joint
with
June
Huh.