ICTP MATH ASSOCIATES SEMINAR (ZOOM) - Thursday 30 July, at 16:00 - Luna Lomonaco (IMPA)

[ICTP/math - di Giovannantonio Margherita]

ICTP MATH ASSOCIATES SEMINAR

Starts 30 Jul 2020 16:00
Ends 30 Jul 2020 17:00
Central European Time
Zoom Meeting

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Speaker: Luna Lomonaco (IMPA)

Title: Mating quadratic maps with the modular group

Abstract: Holomorphic correspondences are polynomial relations P(z,w)=0,
which can be regarded as multi-valued self-maps of the Riemann sphere
(implicit maps sending z to w). The iteration of such multi-valued map
generates a dynamical system on the Riemann sphere (dynamical system which
generalise rational maps and finitely generated Kleinian groups). We
consider a specific 1-(complex)parameter family of (2:2) correspondences
F_a (introduced by S. Bullett and C. Penrose in 1994), which we describe
dynamically. In particular, we show that for every a in the connectedness
locus M_{\Gamma}, this family is a mating between the modular group and
rational maps in the family Per_1(1), and we develop for this family a
complete dynamical theory which parallels the Douady-Hubbard theory of
quadratic polynomials.
This is joint work with S. Bullett.