
## 5. Boundary of $M_d$

1. #### 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]
1. (Want to look at a curve in $M_2$). For $f(z)=\frac{z^2-1}{z^2-c},$ 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.
2. 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.