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University of Cambridge > Talks.cam > Number Theory Seminar > Effective bounds on S-integral preperiodic points for polynomials

## Effective bounds on S-integral preperiodic points for polynomialsAdd to your list(s) Download to your calendar using vCal - Marley Young (University of Cambridge)
- Tuesday 18 October 2022, 14:30-15:30
- Centre for Mathematical Sciences, MR13.
If you have a question about this talk, please contact Rong Zhou. Through an analogy between torsion points on abelian varieties, and preperiodic points (points which eventually enter a cycle under iteration) of rational functions, problems in unlikely intersections motivated 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 integrality condition. This conjecture remains open, and has only been proved (a) in the case very special maps, and (b) under certain local conditions. I will discuss how to obtain effective results in the latter context (following work of Petsche), and how to compute explicit bounds in the case of a unicritical polynomial. This talk is part of the Number Theory Seminar series. ## This talk is included in these lists:- All CMS events
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