Phylogenetic complexity of group-based models

In algebraic statistics, Jukes-Cantor and Kimura models are of great importance. Sturmfels and Sullivant generalized these models associating to any finite abelian group a family of toric varieties. In this talk, we will sketch how to prove that the ideals of these toric varieties are generated in bounded degree (which only depends on the group). For the Kimura 3-parameter model, we show that these ideals are generated in degree at most four.