Title: Wronskians of polynomials
| Speaker: | Kevin Purbhoo |
| Affiliation: | University of Waterloo |
| Room: | MC 5417 |
Abstract:
The Mukhin-Tarasov-Varchenko (MTV) theorem is the following statement in real algebraic geometry. If the wronskian of a set of complex polynomials has only real roots, then the vector space spanned by these polynomials is real. This may seem like innocent curiosity, but it has a variety of applications in geometry, representation theory, and combinatorics. It is also highly non-trivial. Their proof is both a tour de force, and mindbogglingly complicated.
Recently
Jake
Levinson
and
I
found
a
new
way
to
prove
the
MTV
theorem.
This
happened
because
we
conjectured
a
generalization,
and
then
noticed
that
the
generalization
is
actually
easier
to
prove
than
the
original
theorem.
I
will
talk
about
what
our
generalization
says,
and
how
it
came
about.