Monday, April 6, 2015 4:00 pm
-
4:00 pm
EDT (GMT -04:00)
Graham Leuschke, Syracuse University
"What
is
a
non-commutative
desingularization?"
A
resolution
of
singularities
replaces
an
algebraic
variety
with
a
smooth
variety
(manifold)
sharing
the
same
rational
functions.
Also
called
a
desingularization,
resolutions
of
singularities
are
fundamental
tools
for
working
with
singular
spaces.
They
are
known
by
Hironaka
to
exist
for
varieties
defined
over
the
complex
numbers,
but
the
question
of
existence
is
still
open
in
general.
One
approach
to
the
annoyance
is
to
give
a
purely
algebraic
definition
of
desingularization
in
terms
of
ring
theory.
The
world
of
commutative
rings
turns
out
to
be
too
small
for
this
purpose,
so
we
are
led
to
the
possibility
of
``non-commutative
desingularizations.''
I
will
briefly
describe
what's
known
about
commutative
desingularizations,
and
what
they're
good
for,
then
some
progress
and
results
on
what
non-commutative
desingularizations
are,
or
at
least
should
be.
M3
3103
Refreshments will be served in MC 5413 at 3:30 p.m. Everyone is welcome to attend.