TOPICS IN COMPLEX DYNAMICS 2021

TRANSCENDENTAL DYNAMICS
AND BEYOND

CONFERENCE:

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This Conference is part of the
IRP LOW DIMENSIONAL DYNAMICAL SYSTEMS AND APPLICATIONS

REGISTRATION FEE

♦ 30 €

Transcendental dynamics and beyond: Topics in Complex Dynamics 2021 (IRP Low dimensional dynamical systems and applications)

Conference

From April 19, 2021
to April 23, 2021

Registration deadline 24 / 04 / 2021

SCHEDULE

BOOKLET

GROUP PICTURE

Conference Information

The conference focusses on iteration of functions in the complex plane in the presence of essential singularities, in one and several dimensions and related topics. Many problems specific for these types of maps have received a lot of attention in the last few years like the understanding of Fatou components or the subsets of the Julia set which escape to infinity. The conference will also emphasize a variety tools from analysis and topology which are involved and developed motivated by these questions. There will be four to five 2-hour minicourses focusing in different tools relevant to transcendental dynamics and given by leading experts in the field. We will enjoy also some invited lectures and numerous contributions by Ph.D. students and recent doctors.

Scientific Committee

Núria Fagella Universitat de Barcelona

Gwyneth Stallard Open University, UK

Dierk Schleicher Aix-Marseille Université

Organizers

Jordi Canela Universitat Jaume I

Núria Fagella Universitat de Barcelona

Antonio Garijo Universitat Rovira i Virgili

Xavier Jarque Universitat de Barcelona

David Martí-Pete University of Liverpool

Mini-Courses

Anna Benini Universita’ di Parma

Dynamics of Transcendental Henon Maps

ABSTRACT

We will outline the main features of dynamics in C^2 as opposed to dynamics over the complex plane. We will then explain some dynamical features of a special class of non-polynomial automorphisms of C^2, called transcendental Henon maps, highlighting similarities with the dynamics of transcendental entire functions in one variable.

Chris Bishop Stony Brook University

Trees, Triangles and Tracts

ABSTRACT

These two lectures will motivate, state and apply a method for constructing holomorphic functions called quasiconformal folding. In the first lecture, I will review the definition and some properties of harmonic measure on planar domains and consider the problem of constructing conformally balanced trees, i.e., planar trees for which every edge gets equal harmonic measure and the two restrictions of harmonic measure to each side of an edge are equal. Such “true trees” are a special case of Grothendieck’s theory of “dessins d’enfants” and correspond in a natural way to polynomials with exactly two critical values. We will address the questions of which trees can be drawn in this way, and what are the possible shapes of such trees. We will end with some connections to polynomial dynamics and Riemann surfaces.

The second lecture considers the analogous connection between infinite planar trees and entire functions with two singular values. I will state the Folding Theorem, which takes an infinite planar tree with certain geometric assumptions, and returns an entire function with two singular values. I will sketch the idea of the proof, and then describe some applications of the folding construction to transcendental dynamics, e.g., the construction of wandering domains in the Eremenko-Lyubich class, and the construction of transcendental Julia sets with dimension close to 1 (all transcendental Julia sets have dimension at least 1).

Phil Rippon and Gwyneth Stallard Open University – UK

Harmonic and Subharmonic Functions

ABSTRACT

In the first lecture we’ll give an introduction to the basic properties of harmonic and subharmonic functions and some key results, including the Dirichlet problem,Harnack’s inequality, the maximum principle, harmonic measure and estimates for harmonic measure.

In the second lecture we’ll show how these properties of harmonic and subharmonic functions provide useful tools in proving results in complex dynamics, using examples such as properties of escaping wandering domains, covering properties of annuli, and analysing dynamical behaviour in multiply connected wandering domains.

Invited Talks

Matthieu Astorg Université d’Orléans

Krzysztof Baranski Warsaw University

Luka Boc Thaler University of Ljubljana

Kostya Drach Aix-Marseille University

Adam Epstein Warwick University

Vasiliki Evdoridou Open University – UK

Boguslawa Karpinska Technical University of Warsaw

Kirill Lazebnik University of Toronto

David Martí-Pete Liverpool University

Mónica Moreno-Rocha CIMAT

Dan Nicks University of Nottingham

Artur Nicolau Universitat Autònoma de Barcelona

Han Peters University of Amsterdam

Lasse Rempe Liverpool University

Dierk Schleicher Institut de Mathématiques de Marseille

List of participants

Click to open list

Dan Alexandru Paraschiv	Universitat de Barcelona
Magnus Aspenberg	Lund University
Matthieu Astorg	Institut Denis Poisson
Oscar Bandtlow	Queen Mary University of London
Kuntal Banerjee	Presidency University
Krzysztof Baranski	Warsaw University
Anna Benini	Università di Parma
Walter Bergweiler	Kiel University
Anubrato Bhattacharyya	Presidency University
Fabrizio Bianchi	CNRS – Laboratoire Paul Painlevé
Chris Bishop	Stony Brook University
Cinzia Bisi	University of Ferrara
Luka Boc Thaler	University of Ljubljana
Luka Boc Thaler	University of Ljubljana
Konstantin Bogdanov	Aix-Marseille University
Maxence Brévard	Paul Sabatier University – Toulouse III
Andrew Brown	University of Liverpool
Jack Burkart	Stony Brook University
Jordi Canela	Universitat Jaume I
Melida Carranza	Centro de Investigación en Matemáticas A.C.
Tao Chen	The City University of New York – CUNY
Wu Cheng Fa	Shenzhen University
Julià cufí	Universitat Autònoma de Barcelona
Clara Cufí-Cabré	Universitat Autònoma de Barcelona
Weiwei Cui	Lund University
Neil Dobbs	UCD School of Mathematics
Patricia Domínguez	Benemérita Universidad Autónoma de Puebla
Kostya Drach	Aix-Marseille University
David Drasin	Purdue University
Jorge Duarte	University of Lisbon
Artem Dudko	Institute of Mathematics Polish Academy of Sciences
Paula El Khouri	Imperial College London
Adam Epstein	Warwick University
Alexandre Eremenko	Purdue University
Adrián Esparza-Amador	Pontifical Catholic University of Chile
Bernat Espigulé	Universitat de Barcelona
Vasiliki Evdoridou	The Open University
Núria Fagella	Universitat de Barcelona
Álvaro Fernandez Mora	Universitat de Barcelona
Alastair Fletcher	Northern Illinois University
Robert Florido Llinàs	Universitat de Barcelona
John Fornaess	University of Michigan
Logan Fox	Portland State University
Antonio Garijo	Universitat Rovira i Virgili
J.P.K. Gaudoin	Open University
Daniel Girela	Universidad de Málaga
Adi Glücksam	University of Toronto
Marina Gonchenko	Universitat Politècnica de Catalunya
Ignasi Guillén	Universitat Autònoma de Barcelona
Rod Halburd	University College London
Martin Himmel	Aarhus University
Mi Hu	Not provided
Jiaxing Huang	Shenzhen University
Valentin Huguin	Paul Sabatier University – Toulouse III
Pedro Iván Suarez Navarro	University of São Paulo
Xavier Jarque	Universitat de Barcelona
Anna Jové Campabadal	Universitat de Barcelona
Boguslawa Karpinska	Technical University of Warsaw
Ramanpreet Kaur	University of Delhi
Linda Keen	CUNY Graduate Center
Masashi Kisaka	Kyoto University
Gaurav Kumar	Indian Institute of Technology Guwahati
Kirill Lazebnik	Calthech University
Ming Li	Tohoku University
Eleanor Lingham	Sheffield Hallam University
Josep M Gallegos	Universitat Autònoma de Barcelona
Victor Macia	Universitat de Barcelona
Konstantinos Maronikolakis	University College Dublin
Alejandro Marqués Lobeiras	Universidad de Oviedo
David Martí-Pete	University of Liverpool
Volker Mayer	University Lille 1: Sciences and Technologies
Daniel Meyer	University of Liverpool
Mónica Moreno-Rocha	Centro de Investigación en Matemáticas – CIMAT
Hamid Naderiyan	University of North Texas
Daniel Nicks	University of Nottingham
Artur Nicolau	Univesitat Autònoma de Barcelona
Hongmin Nie	Pontifical Catholic University of Chile
Ratna Pal	IISER Berhampur
Dan Paraschiv	Univesitat de Barcelona
Leticia Pardo Simón	Institute of Mathematics of the Polish Academy of Sciences – IMPAN
Juan Pello García	Universitat de Barcelona
Han Peters	University of Amsterdam
Anand Prakash Singh	Central University of Rajasthan
Guru Prem Prasad M	Indian Institute of Technology Guwahati
Feliks Przytycki	Institut of Mathematics – IMPAN
Bernhard Reinke	Aix-Marseille University
Lasse Rempe	University of Liverpool
Josias Reppekus	University of Rome Tor Vergata
Thomas Richards	University of Warwick
Phil Rippon	Open University
Gustavo Rodrigues Ferreira	Open University
Àlex Rodríguez	Universitat de Barcelona
Mohammad Sajid	Qassim University
Dierk Schleicher	Institut de Mathématiques de Marseille
Sergey Shemyakov	Aix-Marseille University
Mitsuhiro Shishikura	Kyoto University
Sudhir Singh	National Institute of Technology Trichy India
Gwyneth Stallard	Open University
Matteo Tabaro	Imperial College London
Raluca Tanase	Uppsala University
Xavier Tolsa Domènech	Universitat Autònoma de Barcelona
Garima Tomar	Central University of Rajasthan
Athanasios Tsantaris	University of Nottingham
Van Tu Le	Paul Sabatier University – Toulouse III
Patrick, Tuen Wai Ng	University of Hong Kong
Joan Verdera	Universitat Autònoma de Barcelona
James Waterman	University of Liverpool
Mareike Wolff	University of Kiel
Jang-Mei Wu	University of Illinois at Urbana–Champaign
jiang Yan	Hunan Institute of Science and Technology
Fei Yang	Nanjing University
Jonguk Yang	Stony Brook University
Tanran Zhang	Soochow University -Suzhou
Yueyang Zhang	University of Science and Technology Beijing
Michel Zinsmeister	University of Orléans
*Updated April 22, 2021

Poster and contributed talks

Participants have the option to contribute with a talk or with a poster. To apply for talks and/or poster presentation please select the relevant option during the registration process.

Application deadline is April 5, 2021

Resolutions will be sent before April 9, 2021

Grants

In order to increase the number of young researchers participating in this activity, the CRM offers grants to cover the registration fee.

To apply, you must complete the registration process, please go to SIGN IN, indicate in the OTHERS section that you wish to apply for a registration grant, you will be asked to attach your CV. Please click on the Reservation option before finishing the process.

Application deadline for grants is April 5

Resolutions will be sent by April 9

Funding

This conference is partially funded from the Faculty of Mathematics of UB, the Institute IMUB, the Societat Catalana de Matemàtiques and the research grants from the Spanish ministry MTM2017-86795-C3-3-P and from the Catalan Government 2017 SGR 1374. We are grateful to all of them for their help.