### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

FEBRUARY 6, 2015

**Speaker: **
Vijay Sookdeo, Catholic University

**Title: ***
Integral point in orbits of morphisms on curves
*

**Abstract:**
Let f be a morphism on a curve C, both defined over a number field K. The forward orbit of a point P on C under f is the collection of all images P, f(P), f(f(P)), etc.; the backward orbit P under f is the collection of all pre-images of P. A theorem of J. Silverman gives a condition for when the forward orbit of P contains at most finitely many points with integral coordinates. We will introduce a conjecture for when the backward orbit of P contains at most finitely many integral points, and discuss results towards this conjecture.

**Time:** Friday, February 6, 2015, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491