Yulan Qing (University of Tennessee) : Gromov boundary generalized.

In this talk we discuss a generalization of the Gromov boundary. We first recall the construction of the sublinearly Morse boundary, which is a metrizable and QI-invariant topological space that enjoys many genericity properties. We then develop the quasi-redirecting boundary and show that it contains the sublinearly Morse boundary as a topological subspace and enjoys the added benefit of being compact in many cases.  More specifically, We show that if X is an asymptotically tree-graded space with mono-directional subsets(ATM), then the quasi-redirecting boundary of X is a compact, metrizable and  quasi-isometrically invariant topological space. Lastly, we show the Quasi-redirecting boundary of the Croke-Kleiner space contains a new and surprising set of QI-invariant directions. This is based on joint work with Kasra Rafi.