BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Minimal models for rational functions in a dynamical setting - Nil
 s Bruin (Simon Fraser University)
DTSTART:20180220T143000Z
DTEND:20180220T153000Z
UID:TALK98791@talks.cam.ac.uk
CONTACT:Beth Romano
DESCRIPTION:We consider the following conjecture by Silverman:\n\nFor each
  d>=0 there is a constant C(d) such that for each rational function phi(z)
  in Q(z) of degree d>=0 and such that phi^2 is not a polynomial\, and for 
 any alpha in Q\, the orbit\n\nO(phi\,alpha)={alpha\,phi(alpha)\,phi(phi(al
 pha))\,...}\n\ncontains at most C(d) integers if phi is *minimal*.\n\nThis
  conjecture is inspired by uniform boundedness conjectures on the number o
 f integral points on elliptic curves in minimal Weierstrass form.\n\nAs fo
 r elliptic curves\, the conjecture is clearly false without a minimality c
 ondition. In this talk we will explore a suitable notion of minimality and
  a way to compute it. See [Nils Bruin\, Alexander Molnar. Minimal models f
 or rational functions in a dynamical setting. LMS J. Comput. Math. 15 (201
 2)\, 400--417.]
LOCATION:MR13
END:VEVENT
END:VCALENDAR