|Location:||MSRI: Online/Virtual, Simons Auditorium|
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.