Introductory Workshop: Dynamics on Moduli Spaces of Geometric Structures January 20, 2015 - January 23, 2015
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC Secondary Mathematics Subject Classification No Secondary AMS MSC
This minicourse is an introduction to the group of conformal transformations of the sphere. We will focus on its action on the space of non-singleton compact subsets of the sphere.
1. Conformal autosimilarity: we will see that the compact subsets whose orbit is closed are exactly the limit sets of convex cocompact subgroups.
2. Quasicircles: we will see that the compact subsets whose orbit closure contains only Jordan curves are exactly the quasicircles.
3. Minimal orbits: we will construct compact subsets of the sphere whose orbit is not closed but whose orbit closure is minimal.
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