Xiaoheng
Jerry
Wang,
Princeton
University
"Density
of
polynomials
with
squarefree
discriminant"
The
problem
of
the
density
of
squarefree
discriminant
polynomials
is
an
old
one,
being
considered
by
many
people,
and
the
density
being
conjectured
by
Lenstra.
A
proof
has
been
out
of
question
for
a
long
time.
The
reason
it
was
desired
is
that
a
squarefree
discriminant
polynomial
f
immediately
gives
the
ring
of
integers
of
Q[x]=f(x);
so
it's
useful
to
know
that
most
of
the
time
one
can
get
directly
at
the
ring
of
integers.
In
recent
joint
work
with
Manjul
Bhargava
and
Arul
Shankar,
we
counted
the
number
of
polynomials
with
squarefree
discriminant
and
proved
the
conjecture
of
Lenstra.
In
this
talk,
I
will
explain
the
general
strategy
of
the
squarefree
sieve
and
the
speci
c
strategy
to
deal
with
discriminant
which
in
turn
leads
to
counting
integral
orbits
for
a
representation
of
a
non-reductive
group.
MC
5501
Refreshments
will
be
served
in
MC
5501
at
3:30
pm.
Everyone
is
welcome
to
attend.