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 introduce a new tool to this problem, namely linear degenerate flag varieties. Because of their connection to Grassmannians and flag varieties, they offer on the one hand a new approach to the study of tropicalizations of flag varieties. On the other hand we open up new interesting questions concerning tropicalizations of linear degenerate flag varieties, which will also be studied in this project. In addition, we will study possible applications of linear degenerate flag varieties in network coding.
