JISD 2024

School on Interactions between Dynamical
Systems and Partial Differential Equations

JISD 2024

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Advanced course / School

From July 08, 2024
to July 12, 2024

200€ General registration
0€ CRM members / Affiliated / Lecturers

Registration deadline 23 / 06 / 2024

LECTURERS

SCHEDULE

POSTER SESSION & GRANTS

Introduction

The School on Interactions between Dynamical Systems and Partial Differential Equations (JISD) is an international summer school that has taken place at the School of Mathematics and Statistics of the Universitat Politècnica de Catalunya (UPC) since 2002. The last four editions have been held at the Centre de Recerca Matemàtica (CRM).

The JISD is an annual meeting between experts and young researchers in Dynamical Systems and Partial Differential Equations (PDEs). It is designed to encourage and enhance the exchange of knowledge and methods, with the goal of advancing the study of cutting-edge problems in the aforesaid fields of mathematics and with the aim of fostering interaction among the participants. The symposium is aimed at local researchers, as well as scientists from the rest of Spain and foreign countries. It is organized into four advanced courses of about 7 hours and complemented by a poster session by young researchers. Throughout the latest editions, the attendance numbers have ranged between 60 and 100 participants, mostly internationals.

A primary objective of the JISD is to attract talented young researchers who can present a poster to put them in a condition to benefit from exposure to world-leading experts and help them establish working relationships that could prove critical for their short and long-term success. An especially strong effort has been devoted in past years to encourage the participation of undergraduates, PhDs and postdocs from developing countries and, more generally, young researchers who may encounter difficulties in accessing adequate financial support.

JISD PAST EDITIONS

lecturers

Marie-Claude Arnaud: Conformal Dynamics

Université Paris Cité

Abstract: Beyond Hamiltonian and symplectic Dynamics, the conformal dynamics study dynamics that multiply a local symplectic form by a factor that is different from 1. This includes for example Hamiltonian systems with friction term. Even if some tools coming from conservative and symplectic dynamics can be used in this setting, some dissipative phenomena appear in is this setting, as attractors. In this course, we will study the conformal dynamics of both classical symplectic manifolds and their extensions, the locally symplectic manifolds. In particular, in the symplectic setting, we introduce and study the natural generalization of Birkhoff attractor in higher dimension. In the locally symplectic setting, we will explain which relation exists between recurrence properties, shape of the orbits and exponential rate of the linearized dynamics (as Lyapunov exponents).

BIBLIOGRAPHY

WEBSITE

Giovanni Catino: Stable Minimal Hypersurfaces

Politecnico di Milano

Abstract: I will present an overview on the classification problem for stable minimal hypersurfaces in the Euclidean space, starting from the seminal work of Schoen-Simon-Yau in the 70’s to the recent advancements obtained by O. Chodosh and C. Li and by myself in collaboration with P. Mastrolia and A. Roncoroni.

NOTES

WEBSITE

Xavier Ros-Oton: Integro-Differential Elliptic Equations

ICREA – Universitat de Barcelona – Centre de Recerca Matemàtica

Abstract: The aim of this course is to provide an introduction to the regularity theory for integrodifferential elliptic equations. Such a class of equations often arises in Analysis, Probability theory, Mathematical Physics, and in several contexts in applied sciences, and this area of research has attracted great interest in the PDE community in the last 15 years, especially since the first works of Caffarelli and Silvestre on the topic. We will start with the basic theory for linear equations, to then give an overview and prove some results for nonlinear equations, and finally discuss some open problems in this context.

NOTES

WEBSITE

Dmitry Turaev: Wildness and Richness of Chaos

Imperial College London

Abstract: We show how various global and local bifurcations lead to chaos of ultimate richness: one determines, by a simple computation, the effective dimension D of the bifurcational problem (an a priori bound on the number of zero Lyapunov exponents) and then shows that all dynamics possible for all systems in the D-dimensional space can emerge at this bifurcation. The techniques can be applied for constructing deep learning algorithms.

WEBSITE

schedule

	MONDAY July 8th	TUESDAY July 9th	WEDNESDAY July 10th	THURSDAY July 11th	FRIDAY July 12th
9:30 10:00	WELCOME	*Wildness and Richness of Chaos* - Dmitry Turaev Imperial College London	Stable Minimal Hypersurfaces - Giovanni Catino Politecnico di Milano	*Conformal Dynamics* - Marie-Claude Arnaud Université Paris Cité	*Integro-Differential Elliptic Equations* - Xavier Ros-Oton ICREA – Universitat de Barcelona – Centre de Recerca Matemàtica
10:00 11:00	*Integro-Differential Elliptic Equations* - Xavier Ros-Oton ICREA – Universitat de Barcelona – Centre de Recerca Matemàtica
11:00 11:30	COFFEE BREAK		Group picture COFFEE BREAK	COFFEE BREAK
11:30 13:00	*Wildness and Richness of Chaos* - Dmitry Turaev Imperial College London	*Integro-Differential Elliptic Equations* - Xavier Ros-Oton ICREA – Universitat de Barcelona – Centre de Recerca Matemàtica	*Conformal Dynamics* - Marie-Claude Arnaud Université Paris Cité	Stable Minimal Hypersurfaces - Giovanni Catino Politecnico di Milano	11:30 - 12:30 - *Conformal Dynamics* - Marie-Claude Arnaud Université Paris Cité
13:00 15:00	LUNCH				12:45 - 13:45 - *Wildness and Richness of Chaos* - Dmitry Turaev Imperial College London
13:00 15:00	LUNCH				13:45 - 15:45 LUNCH
15:00 16:00	Stable Minimal Hypersurfaces - Giovanni Catino Politecnico di Milano	*Conformal Dynamics* - Marie-Claude Arnaud Université Paris Cité	*Integro-Differential Elliptic Equations* - Xavier Ros-Oton ICREA – Universitat de Barcelona – Centre de Recerca Matemàtica	*Wildness and Richness of Chaos* - Dmitry Turaev Imperial College London
16:15 17:15	*Conformal Dynamics* - Marie-Claude Arnaud Université Paris Cité	Stable Minimal Hypersurfaces - Giovanni Catino Politecnico di Milano	*Wildness and Richness of Chaos* - Dmitry Turaev Imperial College London	*Integro-Differential Elliptic Equations* - Xavier Ros-Oton ICREA – Universitat de Barcelona – Centre de Recerca Matemàtica
17:15 18:45	POSTER SESSION + Wine & Cheese		17:15 - 17:45 - COFFEE BREAK
17:15 18:45	POSTER SESSION + Wine & Cheese		17:45 - 18:45 - Stable Minimal Hypersurfaces - Giovanni Catino Politecnico di Milano

POSTER SESSION INFORMATION

Participants have the option to contribute with a poster presentation. Posters have to measure 841cm x 1189cm (A0).

To apply, please select the relevant option during the registration process.

IMPORTANT: if applying for a poster presentation, it will be necessary to fill in the following JISD 2024 – questionnaire for grant and poster presentation applicants .

Resolutions and the information on how to proceed for payment will be sent by the deadline indicated below:

Deadline: April 28th, 2024.
Resolutions will be sent by May 24th, 2024.

grants

In order to increase the number of young researchers participating in this activity, the CRM offers grants to partially cover the registration fee and lodging on-campus (grant reduced fee: 75€).

To apply, you must complete the registration process. Please go to SIGN IN, on the top of the web, choose the “general registration” and in the OTHERS section the grant you wish to apply for, you will be asked to attach your CV. Please click on the Reservation option before finishing the process.

IMPORTANT: if applying for a grant, it will be necessary to fill in the following JISD 2024 – questionnaire for grant and poster presentation applicants .

Resolutions and the information on how to proceed for payment will be sent by the deadline indicated below:

Application deadline for grants is April 28th, 2024.

Resolutions will be sent by May 24th, 2024.

Organising Committee

Xavier Cabré	ICREA-Universitat Politècnica de Catalunya – CRM
Gyula Csato	Universitat de Barcelona – CRM
Amadeu Delshams	Universitat Politècnica de Catalunya – CRM
Marcel Guàrdia	Universitat de Barcelona – CRM
Tere M. Seara	Universitat Politècnica de Catalunya – CRM

scientific committee

Scott Armstrong	Courant Institute, New York University
Jean Pierre Eckmann	Université de Genève
Jean-Michel Roquejoffre	Paul Sabatier University
Susanna Terracini	Università de Torino

LIST OF PARTICIPANTS

Name	Institution
Xavier Cabré Vilagut	Universitat Politècnica de Catalunya
Albert Mas Blesa	Universitat Politècnica de Catalunya
Gyula Csato	Universitat de Barcelona
Amadeu Delshams i Valdés	Universitat Politècnica de Catalunya
MARCEL GUÀRDIA MUNÁRRIZ	Universitat de Barcelona
Maria Teresa Martinez-Seara Alonso	Universitat Politècnica de Catalunya
Pau Reig Llunell	Centre de Recerca Matemàtica
Joan Solà-Morales	Universitat Politècnica de Catalunya
Joan Hernández García	Universitat Autònoma de Barcelona
Niyaz Tokmagambetov	Centre de Recerca Matemàtica
Santiago Barbieri	Universitat de Barcelona
Kostiantyn Drach	Universitat de Barcelona
Nurbek Kakharman	Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Joaquim Duran i Lamiel	Centre de Recerca Matemàtica
Filippo Paiano	University of Pisa
Qinbo Chen	Nanjing University
Alberto Maione	Centre de Recerca Matemàtica
Olli Saari	Universitat Politècnica de Catalunya
Robert Cardona	Universitat de Barcelona
Joan Verdera	Universitat Autònoma de Barcelona
Alessandro Barone	University of Bologna
Anna Danot	Universitat Autònoma de Barcelona
JOAN MATEU BENNASSAR	Universitat Autònoma de Barcelona
Clara Torres Latorre	Universitat de Barcelona
Jean-Michel Roquejoffre	Toulouse III-Paul Sabatier University
Yannick Sire	Johns Hopkins University
Antoni Burón i Palau	Universitat Politècnica de Catalunya
Frank Trujillo	Centre de Recerca Matemàtica
Alberto Roncoroni	Polytechnic University of Milan
Gerard Codina	Universitat Autònoma de Barcelona
Oriol Velasco Falguera	Universitat Politècnica de Catalunya
GABRIELE ALFONSO	University of Naples Federico II
Miriam Lorenzo	Universitat Politècnica de Catalunya
Adrian Arriaga	National Autonomous University of Mexico
Marina Garcia	Universitat Autònoma de Barcelona
Miguel Garrido	Universitat Autònoma de Barcelona
Gerard Castro López	Universitat Politècnica de Catalunya
Davide Polimeni	University of Turin
César David Romero Mora	Université Paris Dauphine PSL
Mar Giralt Miron
Tomás Sanz Perela	Universitat de Barcelona
Amir khodaeian Karim	Imperial College London
Lorenzo Giaretto	University of Turin
Mingmin ZHANG	Paul Sabatier University - Toulouse III
Trí Minh Lê	Vienna University of Technology
Pau Martín de la Torre	Universitat Politècnica de Catalunya
Ernest Fontich Julià	Universitat de Barcelona
Andrew Clarke	Universitat Politècnica de Catalunya
Renzo Bruera	Universitat Politècnica de Catalunya
Matteo Pandolfi	Universitat Politècnica de Catalunya

Registration

The registration fee (200 €/ 75 € for granted) includes coffee breaks and lunch.

You will be asked to create a CRM web user account before registering to the activity through the following link:

CRM USER CREATION

INVOICE/PAYMENT INFORMATION

IF YOUR INSTITUTION COVERS YOUR REGISTRATION FEE: Please note that, in case your institution is paying for the registration via bank transfer, you will have to indicate your institution details and choose “Transfer” as the payment method at the end of the process.

UPF | UB | UPC | UAB

*If the paying institution is the UPF / UB/ UPC / UAB, after registering, please send an email to comptabilitat@crm.cat with your name and the institution internal reference number that we will need to issue the electronic invoice. Please, send us the Project code covering the registration if needed.

Paying by credit card

IF YOU PAY VIA CREDIT CARD but you need to provide the invoice to your institution to be reimbursed, please note that we will also need you to send an email to comptabilitat@crm.cat providing the internal reference number given by your institution and the code of the Project covering the registration (if necessary).

LODGING INFORMATION

ON-CAMPUS AND BELLATERRA

BARCELONA AND OFF-CAMPUS

ACKNOWLEDGEMENTS

For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat

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