4 papers · 1 filter
Tropical cluster varieties, phylogenetic trees, and generalized associahedra
Igor Makhlin
We explicitly describe the tropicalization of a type C cluster variety by identifying it with the space of axially symmetric phylogenetic trees. We also study the signed tropicaliz…
Tropical cluster varieties of type C
Igor Makhlin
We explicitly describe the tropicalization of a cluster variety of finite type C, realizing it as the space of axially symmetric phylogenetic trees. We also find all occurring sign…
Tropicalizing binary geometries
Shelby Cox, Igor Makhlin
The type A cluster configuration space, commonly known as , is the very affine part of the binary geometry associated with the associahedron. The tropicalization…
Poset polytopes and pipe dreams: toric degenerations and beyond
Ievgen Makedonskyi, Igor Makhlin
We demonstrate how pipe dreams can be applied to the theory of poset polytopes to produce toric degenerations of flag varieties. Specifically, we present such constructions for mar…