About Me

Hi! I am a participant in the 2025 DIMACS REU.
Mentor
I am working with Professor Chi Li.
Project Description
Cones!
Weekly Updates
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]