Alberto Raffero (Università degli studi di Firenze, Italy) will speak in the geometry seminar on the 30th January. The talk will take place in the Salle de Profs (9th floor, NO) at 13.30pm. Alberto’s title is “Symplectic half-flat 6-manifolds and the Laplacian G_2-flow” and the abstract is below.
A six-dimensional almost Kähler manifold (M,g,J) is said to be symplectic half-flat if its frame bundle admits an SU(3)-reduction by means of a normalized complex volume form Ψ with closed real part. In the first part of this talk, I shall review the main properties of such manifolds and some classes of examples. In the second part, I shall discuss how the Laplacian G_2-flow on the product manifold M x S^1 can be reinterpreted as a set of evolution equations for the symplectic half-flat SU(3)-structure (g,J,Ψ) on M, and I shall describe a class of symplectic half-flat manifolds where explicit solutions of these equations can be given. This is based on recent joint works with Fabio Podestà (Firenze) and Anna Fino (Torino).