Week 2
1 Week 2
This week, I joined the REU program and met my mentor, Professor Feng Luo. We discussed the project and I learned about circle packing on surfaces. I began to understand the background of the project and gave a presentation on the topic for intro presentation day!
I also started reading some notes written by Professor Luo about circle packing which culminated in the proof of the Köbe-Andreev-Thurston theorem. Here is the statement of the theorem:
Theorem 1.1 (Köbe-Andreev-Thurston) Let
be a simplicially-triangulation of 2-sphere. Then there exists a circle packing
on
, unique up to Mobius transformations, whose nerve is isomorphic to the 1-skeleton of
.