New parametric families of graph-associahedra arising in toric topology

In this talk, using the theory of direct families of polytopes developed by V.M.Buchstaber and the author, we introduce sequences of moment-angle manifolds over flag nestohedra $\{M_{n}\}^{\infty}_{n=1}$ such that $M_{n-1}$ is a submanifold and a retract of $M_{n}$ for any $n\geq 2$, and there exists a non-trivial (higher) Massey product $\langle\alpha_{n,1},\ldots,\alpha_{n,k}\rangle$ in $H^*(M_{n})$ with $\dim\alpha_{n,i}=3, 1\leq i\leq k$ for every $2\leq k\leq n$.
Furthermore, we introduce new closed 2-parametric families of graph-\linebreak associahedra, study their combinatorial properties, and find their applications in toric topology by means of V.M.Buchstaber's theory of the differential ring of simple polytopes.
The talk is based in part on a joint work with Victor Buchstaber.