BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:On some unlikely intersections for values and orbits of rational f
 unctions - Alina Ostafe (The University of New South Wales)
DTSTART:20200218T143000Z
DTEND:20200218T153000Z
UID:TALK136876@talks.cam.ac.uk
CONTACT:Jessica Fintzen
DESCRIPTION:For given rational functions f_1\, ... \,f_s defined over a nu
 mber field K\, Bombieri\, Masser and Zannier (1999) proved that the algebr
 aic numbers alpha for which the values f_1(alpha)\,... \, f_s(alpha) are m
 ultiplicatively dependent are of bounded height (unless this is false for 
 an obvious reason). \n\nMotivated by this\, we present recent finiteness r
 esults on multiplicative relations of values of rational functions at argu
 ments restricted to the maximal abelian extension of K. We go even further
  and discuss the presence of multiplicative relations modulo finitely gene
 rated groups\, posing some open questions. If time allows\, we will presen
 t some finiteness results regarding the presence of powers of S-integers i
 n orbits of polynomial dynamical systems.
LOCATION:MR13
END:VEVENT
END:VCALENDAR