A Sampler of Combinatorial Problems on Spheres
| Speaker: | William J. Martin |
|---|---|
| Affiliation: | Worcester Ploytechnic Institute |
| Room: | Mathematics 3 (M3) 3103 |
Abstract:
In
my
first
month
as
a
graduate
student
at
the
University
of
Waterloo,
I
somehow
selected
an
advisor
(and
that
is
a
story
entirely
of
its
own)
and
asked
him
to
give
me
a
paper
to
read.
Chris
Godsil
gave
me
a
paper
in
which
he
proved
that,
aside
from
complete
multipartite
graphs,
there
are
finitely
many
distance-regular
graphs
having
an
eigenvalue
of
any
given
multiplicity
$m\ge
3$.
This
exploration,
and
a
visit
to
Waterloo
by
Jaap
Seidel
in
May
1989,
had
a
lasting
impact
on
me.
Ever
since,
I
have
been
regularly
interested
in
problems
involving
finite
point
sets
on
the
unit
sphere.
In
this
talk,
I
will
survey
a
few
of
these
problems.
I
will
start
with
some
of
the
more
famous
problems
such
as
the
kissing
number
problem
and
the
equiangular
lines
problem.
Then
I
will
mention
a
few
problems
from
my
own
work,
including
a
minimum
distance
bound
for
error-correcting
codes,
the
dual
Bannai-Ito
Conjecture,
real
mutually
unbiased
bases,
and
systems
of
almost
orthogonal
vectors.
Various
applications
will
appear
throughout
the
talk.