We study existence and regularity of harmonic maps between 2-dimensional simplicial complexes. This work begins by defining metrics on these simplicial complexes and describing their …
Broadly, topology is the study of shapes. In this thesis we specifically study surfaces through graphs which are defined by characteristics of the surface. The …
In a celebrated paper published in 1983, R. Mañé, P. Sad, and D. Sullivan proved a result about holomorphic families of injections called the λ-Lemma …
This thesis explores transversality between algebraic varieties and linear subspaces in the setting of finite fields. The main contributions are effective Bertini-type results for smooth …