Barcelona Algebraic Topology Group
Friday's Topology Seminar 20192020 



Written by Natàlia Castellana Vila

Friday, 06 September 2019 09:39 
Speaker: Luis Javier Hernández Paricio (Universidad de La Rioja) Title: Endomorphisms of the Hopf fibration and numerical methods Place: Room Seminar C3b Date: Wednesday November 13th, 10:00
Abstract: We have developed and implemented in Julia language a collection of algorithms for the iteration of a rational function that avoids the problem of overflows caused by denominators close to zero and the problem of indetermination which appears when simultaneously the numerator and denominator are equal to zero. This is solved by working with homogeneous coordinates and the iteration of a homogeneous pair of bivariate polynomials.
This homogeneous pair induces in a canonical way a selfmap of the pointed Hopf fibration. Moreover, if the homogenous pair is irreducible, we also have a selfmap of the standard Hopf fibration. We study the points of indeterminacy evaluating a canonical map associated with a homogeneous pair on the orbit of a point of the Riemann sphere.
These algorithms can be applied to any numerical method that builds a rational map to find the roots of an univariate polynomial equation. In particular with these procedures we analyze the existence of multiple roots for the Newton method and the relaxed Newton method.
This project is being developed together with J.I. Extremiana, J. M. Guti\'errez and M. T. Rivas (University of La Rioja).
See the calendar for upcoming events.

Last Updated on Tuesday, 05 November 2019 11:29 
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This is the web site of the Algebraic Topology Team in Barcelona (Grup de Topologia Algebraica de Barcelona, 2014SGR42 and Homotopy theory of algebraic structures, MTM201680439P).
Our research interests include a variety of subjects in algebraic topology, group theory, homological algebra, and category theory. Here you will find information about us and our common activities. 

