# On solitons for the closed G2-Laplacian flow. Special Session on the Geometry of Differential Equations. Joint Mathematics Meetings. January 17, 2020

Invited Talk

For G2-structures on 7-manifolds, there is a natural analog of the Ricci-flow studied in Riemannian geometry, namely, one considers a 1-parameter family σ = σ(t) of G2-structures on a given 7-manifold that satisfies the equation dσ/dt = ∆σ with a specified initial G2-structure σ(0) = σ0. When the 1-parameter family σ moves by diffeomorphism and scaling, we say that σ is a soliton for the G2-Laplacian flow. The most interesting case is when the initial G2-structure is closed. In this talk, I will describe some of what is known about the existence and local generality of solitons for this flow, concluding with a discussion of the still-unsolved problem of the generality of the gradient solitons, which are of great interest in the theory of G2-structures.

### Service Performed By

- Bryant, Robert Phillip Griffiths Professor of Mathematics

### Date

- January 17, 2020

### Service or Event Name

- Special Session on the Geometry of Differential Equations

### Host Organization

- Joint Mathematics Meetings

### Location or Venue

- Denver, CO