Title: Higher resonance varieties of matroids
| Speaker: | Graham Denham |
| Affiliation: | University of Western Ontario |
| Room: | MC 6486 |
Abstract:
Resonance
varieties
are
cohomological
invariants
of
topological
spaces;
in
the
case
of
a
complex
hyperplane
arrangement
complement,
however,
the
resonance
varieties
are
determined
by
the
underlying
matroid.
The
combinatorics
of
this
mechanism
is
quite
subtle,
though.
In
cohomological
degree
1,
a
more
or
less
complete
characterization
is
known
in
terms
of
the
existence
of
certain
Latin
square-like
objects
(multinets),
while
in
higher
degrees,
the
picture
is
much
less
clear.
By
regarding
the
Orlik-Solomon
algebra
as
a
functorial
construction
on
a
suitable
category
of
matroids,
some
additional
structure
and
new
phenomena
become
apparent.
I
will
give
some
motivation
for
thinking
about
this,
and
advertise
some
open
problems.