Some 3-variable Diophantine Equations and Arithmetic Dynamics


Yu Yasufuku

14:00:00 - 15:00:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

We analyze when there are many integral points on P^2 with respect to a divisor. This problem is equivalent to asking when there are many solutions to certain Diophantine equations in three variables. Our proof is based on classification of surfaces by the logarithmic kodaira dimension, but some subtly arises when this dimension is equal to 1. In this case, we use Campana's philosophy as the guideline. We apply our result to show that a morphism on P^2 having infinitely many integral points in an orbit must have a nonempty completely invariant set. This is a joint work with Aaron Levin (Michigan State).