Week 0

Much of my first week was spent understanding the "developing map" \( f : S \setminus \Sigma \rightarrow \bar{C} \) we get by specifying a base-point on \(S \setminus \Sigma\), that a Riemann surface of constant Gaussian curvature 1 with a discrete set of (cone) singularities removed, as well as this map's associated monodromy.

This was somewhat nontrivial; my knowledge of Riemann surfaces prior to some recent reading was not particularly good, and so there was a lot to do. I, however, found the appropriate things to read and canonized them in a TeX-ed pdf which is available below.

On Friday, I began the endeavor of using my new knowledge to really understand Eremenko's survey, which I had only previously skimmed. I anticipate this will take me some time and likely a Sunday, so I'll write an addendum after that and before next week!

Read about monodromy here.

Week 1

[Update for Week 1]

Week 2

[Update for Week 2]

Week 3

[Update for Week 3]

Week 4

[Update for Week 4]

Week 5

[Update for Week 5]

Week 6

[Update for Week 6]

Week 7

[Update for Week 7]

Week 8

[Update for Week 8]