Jingyin Huang, The Ohio State University. Morse Quasiflats

We are motivated by looking for traces of hyperbolicity in a space or group which is not Gromov-hyperbolic. One previous approach in this direction is the notion of Morse quasigeodesics, which describes "negatively-curved" directions in the spaces; another previous approach is "higher rank hyperbolicity" with one example being that though triangles in products of two hyperbolic planes are not thin, tetrahedrons made of minimal surfaces are "thin". We introduce the notion of Morse quasiflats, which unifies these two seemingly different approaches and applies to a wider range of objects. In the talk, we will provide motivations and examples for Morse quasiflats, as well as a number of equivalent definitions and quasi-isometric invariance (under mild assumptions). We will also show that Morse quasiflats are asymptotically conical, and comment on potential applications. Based on joint work with B. Kleiner and S. Stadler.