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Anna Fino: Lectures

May 13, 2024
TITLE: Strong G2-structures with torsion

ABSTRACT: A 7-manifold with a G_2-structure \varphi admits a G_2-connection with totally skew-symmetric torsion if and only if d * \varphi = \theta \wedge * \varphi, where \theta is the Lee form of the G_2-structure.

In the talk, I will present recent results on 7-manifolds admitting a G_2-connection with closed totally skew-symmetric torsion. In particular, I will discuss the twisted G_2 equation, which represents the G_2-analogue of the twisted Calabi-Yau equation for SU(n)-structures introduced by Garcia-Fernández, 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_2-structures

ABSTRACT: Closed G_2-structures on 7-manifolds are defined by a closed positive 3-form. Although linear, the closed condition for a G_2-structure is very restrictive, and no general results on the existence of closed G_2-structures on compact 7-manifolds are known.

In the seminar after an introduction on G_2-structures, I will review known examples of compact 7-manifolds admitting a closed G_2-structure. Moreover, I will discuss some results on exact G_2-structures and the behaviour of the Laplacian G_2-flow.

September 10, 2018
TITLE: Compact 7-manifolds with closed G2-structures

ABSTRACT: After reviewing the known examples of compact 7-manifolds admitting a closed G_2-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 G_2-orbifold resolutions.
Moreover, I will show the existence of associative calibrated (hence volume-minimizing) 3-tori with respect to this new closed G_2-structure and, for each of those 3-tori, I will show a 2-dimensional family of non-trivial 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 G_2-flow starting from a closed G_2-structure whose induced metric satisfies suitable extra conditions. In particular we consider the cases when the induced metric is warped or the G_2-structure is extremally Ricci pinched.
The talk is based on joint work with Alberto Raffero.

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