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

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

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Conference
From April 19, 2021
to April 23, 2021
Registration deadline 24 / 04 / 2021
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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.

Collaborators 

 

For inquiries about the activity please contact the research programs coordinator Ms. Núria Hernández at nhernandez@crm.cat​​