**
Khoa
Nguyen,
University
of
British
Columbia
and
Pacific
Institute
for
the
Mathematical
Sciences**

"Dynamical
Analogue
of
Results
by
Bombieri-Masser-Zannier
and
Habegger"

First,
we
briefly
explain
how
results
and
questions
in
diophantine
geometry
give
rise
to
interesting
problems
in
arithmetic
dynamics.
Then
we
focus
on
dynamical
analogue
of
the
following
results
by

Bombieri,
Masser,
Zannier
and
Habegger.

In
1999,
Bombieri,
Masser
and
Zannier
prove
that
if
a
curve
C
in
Gn

m(
Q)
is
not
contained
in
any
translate
of
a
(proper)
algebraic
subgroup
then
the
intersection
of
C
with
the
union
of
all
algebraic
subgroups
of
codimension
1
has
bounded
height.
After
a
series
of
further
work,
they
prove
a
"Structure
Theorem"
and
formulate
a
"Bounded
Height
Conjecture"
which
is
settled
by
Habegger
in
2009.

In 2013, the speaker obtains the first analogue of the above results for the dynamics of self-maps of (P1)n having the form f1x : : :fn where each fi is in Q[t]. Recently, in a joint work with Ghioca, we establish a dynamical analogue of the structure theorem and the more general bounded height theorem by Habegger.

QNC 0101

*
Refreshments
will
be
served
outside
QNC
0101
at
3:30
pm.
Everyone
is
welcome
to
attend.*