Title: Schubert varieties and inversion hyperplane arrangements
| Speaker: | William Slofstra |
| Affiliation: | University of Waterloo |
| Room: | MC 5479 |
Abstract:
Freeness
is
an
interesting
algebraic
property
of
complex
hyperplane
arrangements.
The
standard
examples
of
free
arrangements
are
the
Coxeter
arrangements,
which
consist
of
the
hyperplanes
normal
to
the
elements
of
a
finite
root
system.
It
is
a
natural
(open)
question
to
determine
when
a
subarrangement
of
a
Coxeter
arrangement
is
free.
Surprisingly,
for
the
inversion
subarrangements
this
question
seems
to
be
closely
connected
to
the
combinatorics
of
Coxeter
groups
and
Schubert
varieties.
I
will
talk
about
two
aspects
of
this
connection:
(1)
the
equality
between
the
exponents
of
a
rationally
smooth
Schubert
variety
and
the
exponents
of
the
corresponding
inversion
arrangement,
and
(2)
a
criterion
for
freeness
of
inversion
arrangements
using
root-system
pattern
avoidance.
Much of the talk will be accessible to anyone with knowledge of elementary group theory and linear algebra.