Seminar
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| Location: | SLMath: Online/Virtual, Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
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COMD Stony Brook + MSRI Seminar Series: Boundedness Conjecture For Sierpinski Carpet Hyperbolic Component
To participate in this seminar, please register HERE.
In the early 90s, motivated by known results for Kleinian groups, McMullen conjectured that a hyperbolic component with Sierpinski carpet Julia set is bounded in the moduli space of rational maps. In this talk, we will describe a strategy to attack this problem, and discuss some partial results towards the conjecture. In particular, we will show that
- any geometrically finite degeneration of a Sierpinski carpet hyperbolic component is bounded; and
- any degeneration of a Sierpinski carpet hyperbolic component of disjoint type is bounded.
We will also briefly explain how the techniques can be used to understand the boundaries of more general hyperbolic components.
This talk is partly based on a joint work with Dzmitry Dudko.
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