Your next reading will take a deep dive into conformal geometry and the many ways to discretize and compute conformal maps. This subject makes some beautiful and unexpected connections to other areas of mathematics (such as circle packings, and hyperbolic geometry), and is in some sense one of the biggest “success stories” of DDG, since there is now a complete uniformization theorem that mirrors the one on the smooth side. You’ll find out more about what this all means in the reading! The reading comes from the note, “Conformal Geometry of Simplicial Surface”:
For your assignment you will need to read the Overview (1.1) and Preliminaries (1.2); you must also pick one of Part I, Part II, or Part III to read, each of which covers a different perspective on discrete conformal maps. The most interesting subject, perhaps, is the connections to hyperbolic geometry in Part IV, which you can read for your own enjoyment! 🙂
Hand-in instructions are, as usual, found on the assignments page. The reading is due at 10 AM Eastern, May 3, 2021.