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Algebra Seminar

Thursday, April 6, 2017 - 11:45am

Andrew Obus

U. Virginia and NYU


University of Pennsylvania

DRL 4E19

Second part of a double-header. Note change of day and time.

The dynatomic modular curves parameterize one-parameter
families of dynamical systems on P^1 along with periodic
points (or orbits). These are analogous to the standard
modular curves parameterizing elliptic curves with torsion
points (or subgroups). For the family x^2 + c of quadratic
dynamical systems, the corresponding modular curves are
smooth in characteristic zero. We give several results about
when these curves have good/bad reduction to characteristic
p, as well as when the reduction is irreducible. These results
are motivated by uniform boundedness conjectures in
arithmetic dynamics, which will be explained.
(This is joint work with John Doyle, Holly Krieger,
Rachel Pries, Simon Rubinstein-Salzedo, and Lloyd West.)

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