Special Colloquium

Friday, November 6, 2015 4:00 pm - 4:00 pm EST

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.