
 5/13/2024: Strong G2structures with torsion
 6/09/2022: An overview on closed G_{2}structures
 9/10/2018: Compact 7manifolds with closed G_{2}structures
 6/5/2018: Laplacian flow and special metrics
 5/13/2024: Strong G2structures with torsion
May 13, 2024
TITLE: Strong G2structures with torsion
ABSTRACT: A 7manifold with a G_2structure \varphi admits a G_2connection with totally skewsymmetric torsion if and only if d * \varphi = \theta \wedge * \varphi, where \theta is the Lee form of the G_2structure.
In the talk, I will present recent results on 7manifolds admitting a G_2connection with closed totally skewsymmetric torsion. In particular, I will discuss the twisted G_2 equation, which represents the G_2analogue of the twisted CalabiYau equation for SU(n)structures introduced by GarciaFernández, Rubio, Shahbazi and Tipler. The talk is based on a joint work with Lucia Merchan and Alberto Raffero.
June 9, 2022
TITLE: An overview on closed G_2structures
ABSTRACT: Closed G_2structures on 7manifolds are defined by a closed positive 3form. Although linear, the closed condition for a G_2structure is very restrictive, and no general results on the existence of closed G_2structures on compact 7manifolds are known.
In the seminar after an introduction on G_2structures, I will review known examples of compact 7manifolds admitting a closed G_2structure. Moreover, I will discuss some results on exact G_2structures and the behaviour of the Laplacian G_2flow.
September 10, 2018
TITLE: Compact 7manifolds with closed G_{2}structures
ABSTRACT: After reviewing the known examples of compact 7manifolds admitting a closed structure, I will describe the construction of a new compact example which is formal and has first Betti number b_1=1. The idea of this construction stems from the study of the original Joyce’s techniques on orbifold resolutions.
Moreover, I will show the existence of associative calibrated (hence volumeminimizing) 3tori with respect to this new closed structure and, for each of those 3tori, I will show a 2dimensional family of nontrivial associative deformations.
This is a joint work with Marisa Fernandez, Alexei Kovalev and Vicente Munoz.
June 5, 2018
TITLE: Laplacian flow and special metrics
ABSTRACT: We discuss some results on the behaviour of the Laplacian flow starting from a closed structure whose induced metric satisfies suitable extra conditions. In particular we consider the cases when the induced metric is warped or the structure is extremally Ricci pinched.
The talk is based on joint work with Alberto Raffero.