SPEAKER: Vyron Vellis (UTK)

TITLE: Quasiconformal trees

ABSTRACT: A quasiconformal tree is a doubling metric tree in which the diameter of each arc is bounded above by a fixed multiple of the distance between its endpoints. Quasiconformal trees generalize the well-known notion of quasiarcs. In this talk, inspired by results of Herron-Meyer and Rohde for quasiarcs, we construct a catalog of metric trees in a purely combinatorial way, and show that every quasiconformal tree is bi-Lipschitz equivalent to one of the trees in our catalog. We then discuss how such constructions apply to a special class of metric spaces with good subdivisions. The talk is based on joint work with G. C. David.