Erin Griffin, Syracuse University

Title: Ambient Obstruction Solitons and Homogeneous Gradient Bach Solitons

Abstract: We will discuss a new program of studying ambient
obstruction solitons and homogeneous gradient Bach solitons. We begin
by establishing a number of results for solitons to the geometric flow
for a general tensor, q. Moving on, we prove that any compact ambient
obstruction soliton with constant scalar curvature is trivial. Focusing
on dimension n=4, we show that any homogeneous gradient Bach soliton that
is steady must be Bach flat; that the only homogeneous, non-Bach-flat,
shrinking gradient solitons are product metrics on R² x S² and R² x H²;
and there is a homogeneous, non-Bach-flat, expanding gradient Bach soliton.