Title: Catalan numbers and critical points
| Speaker: | Kevin Purbhoo |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract:
The
Catalan
numbers
are
famously
the
answer
to
a
long
list
of
different
problems
in
enumerative
combinatorics
(binary
trees,
plane
planted
trees,
non-crossing
chord
diagrams,
123-avoiding
permutations,
...
the
list
goes
on
and
on).
After
reviewing
some
of
the
standard
combinatorial
examples,
we
will
consider
an
algebraic
one:
counting
rational
functions
with
prescribed
critical
points.
We
will
then
look
at
some
interesting
connections
between
this
algebraic
example
and
the
combinatorial
ones.
This
is
more
than
just
a
pleasant
collection
of
interconnected
examples.
Putting
everything
together
establishes
the
simplest
case
of
a
deep
theorem
(due
to
Mukhin,
Tarasov
and
Varchenko)
about
real
solutions
to
certainsystems
of
equations.