Colloquium information

Especial Colloquium

Gromov hyperbolicity theory in complex analysis and semigroup-fication of univalent self-maps of the unit disc

Speaker:  Filippo Bracci (Dipartimento di Matematica, Universitá di Roma )
Date:  Wednesday, 15 February 2023 - 12:00
Place:  Aula Naranja, ICMAT

Abstract:

Gromov's theory of hyperbolicity of metric spaces turn out to be very useful in many contexts. In recent years, it has been applied by the speaker and other mathematicians to study dynamical properties of holomorphic self-maps of domains and boundary extension of biholomorphisms. In this talk I will survey some applications for continuous semigroups of holomorphic self-maps of the unit disc and will show how one can naturally associate a semigroup to any given univalent self-map of the unit disc in such a way that such a semigroup has the same dynamical properties of the original map. With this at hand, one can easily prove several results about dynamics and behavior of orbits of univalent functions using the corresponding results for semigroups.

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