Grassmannians and flag varieties are important moduli spaces in algebraic geometry. Understanding their analogues in tropical geometry in terms of a combinatorial characterization is an intriguing but difficult task. In this project, we study this problem with a new tool, namely Quiver Grassmannians resp. linear degenerate flag varieties. We compare tropicalizations and Dressians and study positive parts, short flags and special quivers.
This project aims to make theoretical advancements in the development of a working algorithm as well as to actual implementation of the Minimal Model Program for complex projective klt pairs of log general type. Moreover, we will expand the scope of the famous Cone conjecture beyond the realm of varieties with trivial canonical class.