Wednesday, January 29, 2014 9:30 pm
-
9:30 pm
EST (GMT -05:00)
Determinants, Hyperbolicity and Interlacing
Speaker: | Cynthia Vinzant |
---|---|
Affiliation: | University of Michigan |
Room: | Mathematics and Computer Building (MC) 5158 |
Abstract:
Writing
a
multivariate
polynomial
as
the
determinant
of
a
matrix
of
linear
forms
is
a
classical
problem
in
algebraic
geometry
and
complexity
theory.
Requiring
that
this
matrix
is
Hermitian
and
positive
definite
at
some
point
puts
topological
and
algebraic
restrictions
on
the
polynomials
that
appear
as
the
determinant
and
its
minors.
In
particular
the
real
zero
sets
of
these
polynomials
are
hyperbolic
(or
real
stable)
and
interlace.
I'll
talk
about
the
beautiful
geometry
behind
these
determinants
and
its
connection
to
semidefinite
programming
in
optimization
and
matroid
theory
in
combinatorics.