Quasisymmetries of Sierpinski carpets
Time and place
1 PM on Tuesday, February 26th, 2013; NAC 6/113
SERGIY MERENKOV (UIUC)
Abstract
Sierpinski carpets are topological spaces homeomorphic to the standard Sierpinski carpet, shown here. The topological properties of Sierpinski carpets have been well understood since 1950’s. When Sierpinski carpets arise in various settings, e.g., as boundaries at infinity of Gromov hyperbolic groups, Julia sets of rational functions, etc., they can often be endowed with natural metrics. Such metrics usually carry information about the corresponding structures, e.g., the group or the dynamics in the examples above. This presents the need to investigate metric deformations of Sierpinski carpets. In my talk I plan to discuss quasisymmetric geometry of Sierpinski carpets. I will first define Sierpinski carpets and quasisymmetric deformations, motivating the definitions along the way. Next, I will state important questions and conjectures in the field. Finally, I plan to go over recent results.
