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The Modular Mandelbrot Set

Adventurous Berkeley Complex Dynamics May 02, 2022 - May 06, 2022

May 05, 2022 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Luciana Luna Anna Lomonaco (Institute of Pure and Applied Mathematics (IMPA))
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

The Modular Mandelbrot Set


The Modular Mandelbrot set is the connectedness locus of a family of (2:2) correspondences (introduced by Bullett and Penrose in 1994). We show that these correspondences are matings between the modular group and the family of quadratic rational maps P_A(z)=z+1/z+A, and that there exists a dynamical homeomorphism between the modular Mandelbrot set and the parabolic Mandelbrot set (this last being the connectedness locus of the family P_A(z), and is itself homeomorphic to the classical Mandelbrot set by a result of Petersen and Roesch). The talk is based on joint work with Shaun Bullett.

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The Modular Mandelbrot Set

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