Phylogenetic invariants for group-based models AS2012 Special Volume, part 1: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012. phylogenetic tree group-based model phylogenetic invariant In this paper we investigate properties of algebraic varieties representing group-based phylogenetic models. We propose a method of generating many phylogenetic invariants. We prove that we obtain all invariants for any tree for the two-state Jukes-Cantor model. We conjecture that for a large class of models our method can give all phylogenetic invariants for any tree. We show that for 3-Kimura our conjecture is equivalent to the conjecture of Sturmfels and Sullivant [22, Conjecture 2]. This, combined with the results in [22], would make it possible to determine all phylogenetic invariants for any tree for 3-Kimura model, and also other phylogenetic models. Next we give the (first) examples of non-normal varieties associated to general group-based model for an abelian group. Following Kubjas [17] we prove that for many group-based models varieties associated to trees with the same number of leaves do not have to be deformation equivalent. Donten-Bury, Maria Michalek, Mateusz 2012 2012 Article application/pdf islandora:1007827 http://hdl.handle.net/10560/islandora:1007827 MATH / Applied Mathematics Illinois Institute of Technology Journal of Algebraic Statistics en Open Access