Title: Permuto-associahedra as deformations of nested permutohedra 

Abstract: A classic problem connecting algebraic and geometric combinatorics is the realization problem: given a poset (with a reasonable structure), determine whether there exists a polytope whose face lattice is the poset. In the 1990s, Kapranov defined a poset, called the permuto-associhedron, as a hybrid between the face poset of the permutohedron and the associahedron, and he asked whether this poset is realizable. Shortly after his question was posed, Reiner and Ziegler provided a realization. In this talk, I will discuss a different construction we obtained as a deformations of nested permutohedra. This is joint work with Federico Castillo.