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JISD 2025

21st School on Interactions between Dynamical Systems and Partial Differential Equations

JISD 2025

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Advanced course / School
From June 30, 2025
to July 04, 2025

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

Registration deadline 12 / 06 / 2025

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 five 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 position 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

AVERAGING AND FERMI ACCELERATION

Dmitry Dolgopyat

University of Maryland

Abstract: Averaging is one of classical tools in dynamics. However, despite two centuries of work, there are still many open problems. In this course I will illustrate some recent results and open problem in a model case of Fermi acceleration where one would like to describe the evolution of energy for a particle with the environment.

WEBSITE

NONLOCAL MINIMAL SURFACES

Serena Dipierro

University of Western Australia

Abstract: We present the theory of nonlocal minimal surfaces, with special attention to interior regularity, sheeting phenomena, maximum principle, boundary stickiness and connection with phase transitions.

WEBSITE

RIGIDITY RESULTS AND BOCHNER TYPE TECHNIQUES IN RIEMANN GEOMETRY

Luciano Mari

Università degli Studi di Milano Statale

Abstract: This minicourse aims to introduce some techniques used to prove splitting and topological/geometric rigidity theorems in Riemannian Geometry. I will highlight how the stability/finite index of a Schrodinger operator naturally appearing in the problem forces the rigidity phenomenon. Among the applications, time permitting I will discuss some results in Schoen-Yau’s theory of harmonic maps,

Li-Tam-Wang’s theory of Harmonic functions, and minimal (hyper)surfaces.

WEBSITE

DYNAMICAL DECOMPOSITIONS OF SURFACE DIFFEOMORPHISMS

Sylvain Crovisier

Université Paris-Saclay

Abstract: In order to describe the dynamics of a diffeomorphism, one first try to decompose the system into invariant elementary pieces, that may be studied separately. For hyperbolic dynamics, the decomposition is provided by Smale’s « spectral decomposition theorem », and the number of pieces is finite. These lectures deal with the decomposition of general smooth diffeomorphisms on surfaces.

One will mainly focus on systems which have infinitely many pieces: typical examples have been constructed by Newhouse. Several view points will be covered: topological (filtration, renormalization) or measurable (Borel homoclinic classes). In good cases, the dynamics inside each piece may be studied as for uniformly hyperbolic systems: most of their orbits equidistribute towards natural invariant measures (physical or maximizing the entropy), and their statistics are described by limit theorems. I will also discuss how the dynamics degenerates along sequences of distinct pieces, in terms of their dynamical invariants (e.g. the entropy and the Lya-punov exponents).

WEBSITE

schedule

TBP

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 in the registration process, it will also be necessary to fill in the following JISD 2025 – 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 13, 2025.
  • Resolutions will be sent by May 16, 2025.

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 in the registration process, it will also be necessary to fill in the following JISD 2025 – 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:
The application deadline for grants is April 13, 2025.
Resolutions will be sent by May 16, 2025.
Organising Committee
Xavier Cabré​ ICREA – ​Universitat Politècnica de Catalunya – CRM
Amadeu Delshams​ ​Universitat Politècnica de Catalunya – CRM
Mar Giralt IMCCE at Observatoire de Paris
​Marcel Guàrdia​ ​​Universitat de Barcelona – CRM
Tomás Sanz 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
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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