Title: Counting Maps via Character Theory
| Speaker: | Trevor Gunn |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract:
A map is a 2-cell embedding of a graph in a surface. We discuss how to encode maps in oriented surfaces as triples of permutations. Then, using the representation theory of the symmetric group, we derive a generating function for rooted maps in terms of their face, vertex and edge counts.
We
shall
then
consider
hypermaps
in
orientable
and
locally
orientable
(i.e.
orientable
or
non-orientable)
surfaces.
The
generating
function
for
rooted
hypermaps
in
orientable
surfaces
is
given
in
terms
of
Schur
functions.
In
locally
orientable
surfaces,
it
is
in
terms
of
zonal
polynomials.
These
two
classes
of
symmetric
functions
share
a
generalization
in
terms
of
Jack
symmetric
functions
a).
class
of
symmetric
functions
indexed
by
an
indeterminant
b).
It
is
this
combinatorial
lift
that
will
allow
us
to
state
the
b-conjecture
of
I.
P.
Goulden
and
D.
M.
Jackson.
Title: Weighted Low Rank Matrix Approximation
| Speaker: | Wenchao Du |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract:
We
consider
the
generalisation
of
low
rank
matrix
approximation,
where
the
measure
of
distance
is
element-wise
weighted
Frobenius
norm.
This
problem
is
known
to
be
NP-hard,
but
convex
relaxation
via
nuclear
norm
has
been
proposed
for
0-1
weights.
We
explore
possible
extensions
of
this
relaxation
to
the
general
case,
and
compare
against
other
state-of-the-art
optimization
methods.