Milner 317

Wednesdays, 12:30-1:30 PM

Amherst College

**Tuesday,
April 24
Milner 317, 3:00 pm**

**Title: **Another
$n$-point $abc$ conjecture

**Abstract:** We will
interpret the $abc$ conjecture as a statement about four points in the
projective line. For function fields of characteristic zero,
where the $abc$ conjecture is a theorem, we will consider
generalizations corresponding to $n$ points in the projective
line. Analogous conjectures can then be made for number
fields. We will also consider applications of such conjectures to
arithmetic problems, such as Morton and Silverman's conjecture that
there is a uniform bound for the number of rational preperiodic points
of a morphism defined over a number field.