CONSTRUCTING SOLITONS FOR AN ISOMETRIC FLOW ON G_2 STRUCTURES - THOMAS IVEY (COLLEGE OF CHARLESTON)
G_2 structures arise naturally when a 7-dimensional Riemannian manifold M carries a distinguished positive differential 3-form f. A G_2-structure endows the manifold with an orientation and Riemannian metric g. (Thus, the pointwise automorphism group of f is isomorphic to a compact subgroup of SO(7).) A G_2-structure is torsion-free if f is parallel with respect to the Levi-Civita connection of g, in which case (M,f) is called a G_2-manifold. Non-trivial G_2 manifolds, which have reduced holonomy, are difficult to construct. Inspired by the Ricci flow, several authors have studied evolution equations for G_2 structures, with the hope that these limit to closed or co-closed structures.
This talk concerns a flow on isometric G_2-structures which is the negative gradient flow for total torsion. (Two G_2-structures are said to be isometric if they induce the same metric g.)
The flow was recently introduced by Dwivedi, Giannotis and Karigiannis, who proved long-time existence and convergence to a structure with divergence-free torsion or to a shrinking soliton. In this talk, we construct soliton structures isometric to a fixed torsion-free background such as the canonical flat G_2-structure on R^7 or the product of a Calabi-Yau 3-fold with a circle. The restriction of the flow to structures like these, which have a high degree of symmetry, provides important test cases for convergence. This is joint work with Spiro Karigiannis.
This talk will be presented in a hybrid mode. It will take place at the Aula Seminari (3rd floor) of the Department of Mathematical Sciences "G. L. Lagrange" (Politecnico di Torino), Corso Duca degli Abruzzi 24.
Please, contact the organisers (dgseminar.torino@gmail.com) in order to get the link to attend the talk remotely.
For more information on the seminar and on the schedule of the talks, please visit our website.