As a generalization of hyperbolic groups, the class of acylindrically hyperbolic groups includes many interesting examples and has has received considerable attention. In the world of hyperbolic groups, quasiconvex subgroups are important subjects. What would be a proper analog of quasiconvex subgroups in the context of acylindrically hyperbolic groups? In this talk, I will share my answer to this question and some more questions.

A link of the slides could be find here: https://homepages.math.uic.edu/~pwan5/Talk_GPQC.pdf I might modify it later. If so, I will update the file.