Universal Circles

Foliations, flows, and many other dynamical structures on (hyperbolic) 3-manifolds may be tamed and understood via so-called “universal circles”. Conversely, thinking about such structures in terms of universal circles motivates the definition and study of new objects (Zippers, CaTherine wheels, etc) and creates bridges to adjacent fields of mathematics (uniform quasimorphisms, expanding Thurston maps, SLE(8) curves etc). I will define as many of these structures, and explain as much of the network of sometimes subtle and sometimes conjectural relationships between them, as time allows. No previous knowledge of these subjects is assumed.

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