• • 6/09/2022: An overview on closed G₂-structures
    
  • 9/10/2018: Compact 7-manifolds with closed G₂-structures
    
  • 6/5/2018: Laplacian flow and special metrics
    

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 -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 volume-minimizing) 3-tori with respect to this new closed -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 -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.

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