Effective Uniformization Theorem: A Senior Thesis

Abstract

In this thesis, I present a complete proof of the Effective Uniformization Theorem, proved by Sergiu Klainerman and Jérémie Szeftel in 2019 in their work titled Effective Results on Uniformization and Intrinsic GCM Spheres. In this exposition, I focus on proving numerous intermediate steps that might not be self-evident to the readers, shedding light on various technical results, correcting detected inaccuracies, and increasing the precision of the statements of the original paper.