**Aaron Kennon,
UC Santa Barbara**

**Title:**
Nearly Parallel G_{2}-Structures from the Perspective of Geometric Flows

**Abstract:** A 3-Sasakian structure on a 7-manifold may be used to
define two distinct Einstein metrics: the 3-Sasakian metric and the
squashed Einstein metric. Both metrics are induced by nearly parallel
G_{2}-structures which may also be expressed in terms of the 3-Sasakian
structure. Just as Einstein metrics are critical points for the Ricci
flow up to rescaling, nearly parallel G_{2}-structures provide natural
critical points of the (rescaled) geometric flows of G_{2}-structures
known as the Laplacian flow and Laplacian coflow. We study each of
these flows in the 3-Sasakian setting and see that their behaviour is
markedly different, particularly regarding the stability of the nearly
parallel G_{2}-structures. We also compare the behaviour of the flows
of G_{2}-structures with the (rescaled) Ricci flow.

This is joint work
with Jason Lotay.