Jenia TevelevVogiannou, Anastasios2024-04-262024-04-262016-092016-0910.7275/8487187.0https://hdl.handle.net/20.500.14394/20066In this thesis, I extend tropicalization of subvarieties of algebraic tori over a trivially valued algebraically closed field to subvarieties of spherical homogeneous spaces. I show the existence of tropical compactifications in a general setting. Given a tropical compactification of a closed subvariety of a spherical homogeneous space, I show that the support of the colored fan of the ambient spherical variety agrees with the tropicalization of the closed subvariety. I provide examples of tropicalization of subvarieties of GL(n), SL(n), and PGL(n).spherical varietiestropicalizationcompactificationsAlgebraic GeometrydissertationN/A