Title: Aligned curves and height functions on Jacobians of curves
| Speaker: | Garnet Akeyr |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract:
The
goal
of
this
talk
is
to
define
an
aligned
curve
and
discuss
applications
of
aligned
curves
in
algorithms
for
computing
the
heights
of
points
on
Jacobians
of
curves.
Height
functions
will
be
of
interest
to
those
in
hyperelliptic
cryptography,
where
computing
the
Mordell-Weil
group
of
the
Jacobian
of
a
hyperelliptic
curve
is
an
important
and
difficult
problem.
The
idea
of
an
aligned
curve
deals
with
the
dual
graph
of
a
curve,
which
is
a
graph
in
the
graph-theoretic
sense.
This
will
be
a
high-level
talk
and
should
be
accessible
to
anyone
with
basic
ring
theory.
After
motivating
the
problem
with
examples
from
cryptography,
I
shall
define
an
algebraic
curve
and
all
the
related
notions
needed
to
discuss
aligned
curves.
Open
problems
related
to
height
functions
on
Jacobians
of
hyperelliptic
curves
will
be
discussed
at
the
end.
Relevant paper: http://arxiv.org/abs/1402.0647
For
more
information
about
our
reading
group,
please
visit
our
webpage
http://www.math.uwaterloo.ca/~deolivei/reading.htm