Title:
A
positive
semidefinite
approximation
for
the
cone
of
non-negative
polynomials
(
by
Romero
and
Velasco)
| Speaker: | Julian Romero |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract:
This
is
a
reminder
for
our
next
meeting
that
will
take
place
on
Monday
in
MC6486.
Door
will
open
at
4pm.
As
usual
we
will
have
15
mins
for
socializing
and
for
eating
pizza
before
the
talk
starts
(at
4:15pm
sharp).
Testing
the
non-negativity
of
multivariate
polynomials
is
an
NP-complete
problem
that
has
various
applications,
see
for
example
http://www.princeton.edu/~amirali/Public/Publications/or_isos.pdf
.
In
this
talk
I
will
discuss
a
method
due
to
A.
Barvinok
et.
al.
to
approximate
compact
convex
sets
supporting
a
probability
measure.
The
method
uses
such
measure
to
define
a
sequence
of
spectrahedra
converging
to
the
original
convex
set
and
it
has
the
advantage
of
being
possible
to
calculate
how
close
is
getting
each
element
of
the
sequence
to
the
original
set.
We
will
see
that
this
method
can
be
applied
to
find
semidefinite
approximations
for
the
cone
of
Non-negative
Polynomials
and
I
will
show
some
bounds
on
how
close
these
approximations
are
for
the
cases
of
quaternary
quartics
(polynomials
on
four
variables
of
degree
four)
and
ternary
sextics
(polynomials
on
three
variables
of
degree
six).
The
presentation
will
be
based
on
the
following
manuscripts:
http://arxiv.org/abs/1409.8272
For
more
information
about
our
reading
group,
please
visit
our
webpage
http://www.math.uwaterloo.ca/~k2georgi/reading.htm