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Soliton Solutions of the Laplacian Flow from the Perspective of Exact G2-Structures with Dr. Aaron Kennon from UC Santa Barbara

This is a past event.

Friday, August 26, 2022 at 1:30pm to 2:30pm

DM - Deuxieme Maison, 409A
11200 SW 8th ST, Deuxieme Maison, Miami, Florida 33199

Abstract: Closed G2-Structures are of profound importance for constructing metrics with holonomy G2, however, we know very little about the space of closed G2-Structures on any given compact, orientable, spin 7-manifold. In particular, we do not know if such a compact 7-manifold may admit an exact G2-Structure. We would also like to know more about soliton solutions of the Laplacian flow, which is a geometric flow that aims to provide insight into when we may perturb a G2-Structure with torsion to a torsion-free G2-Structure. We exploit the fact that the G2-Structure underlying a (shrinking or expanding) closed Laplacian soliton is exact to study these solitons as a special class of exact G2-Structure. This approach turns out to be quite powerful as it provides a unified picture for the established results for such solitons in the literature while motivating new results for solitons as special cases of results which hold for exact G2-Structures more generally.

Event Type

Academics, Lectures & conferences

Audience

Students, Faculty & Staff

Department
Department of Mathematics and Statistics
Hashtag

#mathematics

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