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SUMMARY:Effective bounds on S-integral preperiodic points for polynomials 
 - Marley Young (University of Cambridge)
DTSTART:20221018T133000Z
DTEND:20221018T143000Z
UID:TALK180398@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:Through an analogy between torsion points on abelian varieties
 \, and preperiodic points (points which eventually enter a cycle under ite
 ration) of rational functions\, problems in unlikely intersections motivat
 ed S. Ih to conjecture the finiteness of preperiodic points for a rational
  function on P^1\, defined over a number field\, which satisfy a certain i
 ntegrality condition.\n\nThis conjecture remains open\, and has only been 
 proved (a) in the case very special maps\, and (b) under certain local con
 ditions. I will discuss how to obtain effective results in the latter cont
 ext (following work of Petsche)\, and how to compute explicit bounds in th
 e case of a unicritical polynomial.
LOCATION:Centre for Mathematical Sciences\, MR13
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