So far, my research is centered around the Proj construction for rings graded by finitely generated abelian groups. It was introduced by Brenner-Schröer in 2003.
It involves multiple areas of math, like GIT, Toric Geometry, Tropical Geometry, and Birational Geometry. In my thesis, I  mostly focused on GIT and the description of simplicial toric (pre)varieties in terms of the multigraded Proj construction. 

The next logical step would be a systematic analysis of the multigraded Proj construction applied to Cox rings of Mori Dream Spaces.

Thesis

Multihomogeneous Spectra: Multigraded Proj and Multihomogeneous D-Prime Spectra