22 nov 2018 -- 15:30
Aula 5, DiMaI, Firenze
$G_2$-structures defined by a closed positive $3$-form constitute the starting point in various known and potential methods to obtain holonomy $G_2$ metrics. Albeit linear, the closed condition is quite restrictive, and no general results on the existence of closed $G_2$-structures on compact $7$-manifolds are known. In this talk, I shall review some recent results on the construction of compact examples with high degree of symmetry, and I shall discuss the properties of closed $G_2$-structures giving rise to self-similar solutions of the $G_2$-Laplacian flow.