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HOLOGRAM SIGNED

Holomorphic Dynamics connecting Geometry, Root-Finding, Algebra, and the Mandelbrot set

Total Cost €

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EC-Contrib. €

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Partnership

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Project "HOLOGRAM" data sheet

The following table provides information about the project.

Coordinator
TECHNISCHE UNIVERSITAT BERLIN 

Organization address
address: STRASSE DES 17 JUNI 135
city: BERLIN
postcode: 10623
website: www.tu-berlin.de

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Total cost 2˙312˙481 €
 EC max contribution 2˙312˙481 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-AdG
 Funding Scheme ERC-ADG
 Starting year 2016
 Duration (year-month-day) from 2016-10-01   to  2021-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    TECHNISCHE UNIVERSITAT BERLIN DE (BERLIN) coordinator 1˙342˙867.00
2    JACOBS UNIVERSITY BREMEN GGMBH DE (BREMEN) participant 969˙613.00

Map

 Project objective

Dynamical systems play an important role all over science, from celestial mechanics, evolution biology and economics to mathematics. Specifically holomorphic dynamics has been credited as “straddling the traditional borders between pure and applied mathematics”. Activities of numerous top-level mathematicians, including Fields medalists and Abel laureates, demonstrate the attractivity of holomorphic dynamics as an active and challenging research field.

We propose to work on a research project based in holomorphic dynamics that actively connects to adjacent mathematical fields. We work on four closely connected Themes:

A. we develop a classification of holomorphic dynamical systems and a Rigidity Principle, proposing the view that many of the additional challenges of non-polynomial rational maps are encoded in the simpler polynomial setting;

B. we advance Thurston’s fundamental characterization theorem of rational maps and his lamination theory to the world of transcendental maps, developing a novel way of understanding of spaces of iterated polynomials and transcendental maps;

C. we develop an extremely efficient polynomial root finder based on Newton’s method that turns the perceived problem of “chaotic dynamics” into an advantage, factorizing polynomials of degree several million in a matter of minutes rather than months – and providing a family of rational maps that are highly susceptible to combinatorial analysis, leading the way for an understanding of more general maps;

D. and we connect this to geometric group theory via “Iterated Monodromy Groups”, an innovative concept that helps solve dynamical questions in terms of their group structure, and that contributes to geometric group theory by providing natural classes of groups with properties that used to be thought of as “exotic”.

 Publications

year authors and title journal last update
List of publications.
2019 KHUDOYOR MAMAYUSUPOV
A characterization of postcritically minimal Newton maps of complex exponential functions
published pages: 2855-2880, ISSN: 0143-3857, DOI: 10.1017/etds.2017.137
Ergodic Theory and Dynamical Systems 39/10 2019-09-26
2017 Dierk Schleicher, Robin Stoll
Newton\'s method in practice: Finding all roots of polynomials of degree one million efficiently
published pages: 146-166, ISSN: 0304-3975, DOI: 10.1016/j.tcs.2017.03.025
Theoretical Computer Science 681 2019-09-26
2018 Khudoyor Mamayusupov
Newton maps of complex exponential functions and parabolic surgery
published pages: 265-290, ISSN: 0016-2736, DOI: 10.4064/fm345-9-2017
Fundamenta Mathematicae 241/3 2019-09-26
2019 KOSTIANTYN DRACH, YAUHEN MIKULICH, JOHANNES RÃœCKERT, DIERK SCHLEICHER
A combinatorial classification of postcritically fixed Newton maps
published pages: 1-32, ISSN: 0143-3857, DOI: 10.1017/etds.2018.2
Ergodic Theory and Dynamical Systems 2019-09-26
2017 Konstantin Bogdanov, Khudoyor Mamayusupov, Sabyasachi Mukherjee, Dierk Schleicher
Antiholomorphic perturbations of Weierstrass Zeta functions and Green’s function on tori
published pages: 3241-3254, ISSN: 0951-7715, DOI: 10.1088/1361-6544/aa79cf
Nonlinearity 30/8 2019-09-26
2018 Laurent Bartholdi, Dzmitry Dudko
Algorithmic aspects of branched coverings I/V. Van Kampen’s theorem for bisets
published pages: 121-172, ISSN: 1661-7207, DOI: 10.4171/ggd/441
Groups, Geometry, and Dynamics 12/1 2019-09-26
2018 Mikhail Hlushchanka, Daniel Meyer
Exponential growth of some iterated monodromy groups
published pages: 1489-1518, ISSN: 0024-6115, DOI: 10.1112/plms.12118
Proceedings of the London Mathematical Society 116/6 2019-09-26
2017 Dierk Schleicher
Internal Addresses of the Mandelbrot Set and Galois Groups of Polynomials
published pages: 1-35, ISSN: 2199-6792, DOI: 10.1007/s40598-016-0042-x
Arnold Mathematical Journal 3/1 2019-09-26
2017 Henk Bruin, Dierk Schleicher
Hausdorff dimension of biaccessible angles for quadratic polynomials
published pages: 201-239, ISSN: 0016-2736, DOI: 10.4064/fm276-6-2016
Fundamenta Mathematicae 238/3 2019-09-26
2019 Roman Chernov, Kostiantyn Drach, Kateryna Tatarko
A sausage body is a unique solution for a reverse isoperimetric problem
published pages: 431-445, ISSN: 0001-8708, DOI: 10.1016/j.aim.2019.07.005
Advances in Mathematics 353 2019-09-26
2018 Laurent Bartholdi, Dzmitry Dudko
Algorithmic aspects of branched coverings IV/V. Expanding maps
published pages: 7679-7714, ISSN: 0002-9947, DOI: 10.1090/tran/7199
Transactions of the American Mathematical Society 370/11 2019-09-26
2017 Laurent Bartholdi, Dzmitry Dudko
Algorithmic aspects of branched coverings
published pages: 1219-1296, ISSN: 0240-2963, DOI: 10.5802/afst.1566
Annales de la faculté des sciences de Toulouse Mathématiques 26/5 2019-09-26

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