Department of Mathematics

Speaker: Pekka Pankka
Title: Almost Sure Limits of Some Manifolds and Graphs
Affiliation: Academy of Finland
Date: Thursday, April 19, 2012
Place and Time: Room 107 LOV, Love Building, 3:35-4:30 pm

Abstract. Consider a sequence of closed Riemannian manifolds so that the diameters of manifolds grow without bounds. Using the Gromov-Hausdorff convergence of manifolds we may consider the collection of all limits of subsequences of this sequence. But what are they typically like? Quite surprisingly, under an additional geometric assumption of quasiconformal nature, the limit is almost surely (in a suitable sense) quasiconformally equivalent either to the Euclidean space or once puncture Euclidean space. In this talk I will discuss this result and its relation to the work of Benjamini and Schramm on circle packings and distributional limits of finite planar graphs. This is joint work with Hossein Namazi and Juan Souto.