5. Boundary of $M_d$

Problem 5.1.
[Rachel Pries] Give an algebraic description of the boundary and maps in the boundary in characteristic $p$ not necessarily $0.$ (Reference DeMarco). Try $d=3.$ Motivation: results for moduli curves use understanding of the boundary. 
Problem 5.2.
[Holly Krieger] (Want to look at a curve in $M_2$). For $f(z)=\frac{z^21}{z^2c},$ there is a collection of PCF maps which approach $c=1$ on the curve. Compare the arboreal representation for $f$ to the representation of the limit map.
 More generally, how do these representations behave as you deform to the boundary?
Cite this as: AimPL: The Galois theory of orbits in arithmetic dynamics, available at http://aimpl.org/galarithdyn.