Likely intersections for forward orbits of curves

Speaker: Jit Wu Yap, graduate student, Harvard University

Time: 15:00-16:00, May 16

Venue: Room 102, School of Mathematical Sciences, Zijingang Campus

Abstract: Let $f,g$ be two polynomials of degree $d > 1$ and let $\varphi = (f,g)$ be the endomorphism acting on $P^1 x P^1$. Given two curves $C$  and  $C'$,  we  expect  that  the  forward  iterates  of  $C$,  given  by $\varphi^n(C)$, to intersect $C'$ at many distinct points. We show that outside  of  some   exceptional   cases,   this  is  true  under  a  technical assumption of the Julia sets of $f$ and $g$. This is joint work with Sina Saleh.