18th School on Interactions Between Dynamical Systems and Partial Differential Equations (JISD2022)

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Advanced course / School
From June 27, 2022
to July 01, 2022
Registration deadline 05 / 06 / 2022



Organised in partnership with the  Clay Mathematics Institute

NOTE: If you just want to pre-register now and pay later or apply for a grant, select the following options during the registration process:

  • Price: 250 EUR (50 EUR for those applying for a grant)
  • Invoice: No invoice
  • Grants: if you ask for a grant, attach your CV
  • Summary: Reservation as your payment method


The School on Interactions between Dynamical Systems and Partial Differential Equations (JISD) is an international summer school that takes place at the School of Mathematics and Statistics of the Universitat Politècnica de Catalunya (UPC) since 2002. The last three 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 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 the 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 condition to benefit from the 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 an adequate financial support. 

Lecturers & Courses

Analysis of the nonlocal conformal invariant variational problems, by Prof. Francesca Da Lio (ETH Zürich, Switzerland​)
There has been a lot of interest in recent years for the analysis of free-boundary minimal surfaces. In the first part of the course I will recall some facts of conformal invariant problems in 2D and some aspects of the integrability by compensation theory . In the second part I will show how this theory can be extended to the nonlocal framework
Variational and Differential Geometric Methods in the N-body problem, by Prof. ​Richard Montgomery​ (​University of California, Santa Cruz, USA)
We cover variational and differential geometric methods for the N-body problem. We begin with W. Gordon’s theorem regarding the direct method of the Calculus of Variations as it applies to the Kepler problem. We then describe how the direct method led to the figure eight solution and other choreographies. In the process we describe the direct method, Marchal’s lemma, the imposition of symmetries and shape space. Shape space is the quotient of N-body configuration space by the group of rigid motions. To obtain the figure eight Chenciner and I did most of our work on shape space. The projection to shape space, at least for the planar problem and away from total collision, is an example of a Riemannian submersion. We do not assume the audience knows what these submersions are, so part of the mini-course will developing them, the related concept of a fiber bundle, and the intuition and usefulness of these geometric structures in the N-body problem.I plan to end by describing several open problems suggested by a topological and metric perspective on the N-body problem.   
Perturbation theories versus canonical coordinates in celestial mechanics, by Prof. Gabriella Pinzari (University of Padova, Italy)
KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by V.I.Arnold in the 60s who worked out a theorem, that he named the “Fundamental Theorem”, especially designed for the planetary problem. This is the problem of 1+n point masses, one “sun” and n “planets”, undergoing gravitational attraction. However, Arnold’s Fundamental Theorem could be really used at that purpose only when, about 50 years later, the “right” canonical set was discovered. In these lectures I shall talk about the complex interplay between perturbation theories and canonical coordinates in problems of celestial mechanics.    
Minmax Methods in the Calculus of Variations of Curves and Surfaces, by Prof. Tristan Rivière (ETH Zürich, Switzerland)
The study of the variations of curvature functionals takes its origins in the works of Euler and Bernouilli from the eighteenth century on the Elastica. Since these very early times, special curves and surfaces such as geodesics, minimal surfaces, elastica, Willmore surfaces, etc. have become central objects in mathematics much beyond the field of geometry stricto sensu with applications in analysis, in applied mathematics, in theoretical physics and natural sciences in general. Despite its venerable age the calculus of variations of length, area or curvature function- als for curves and surfaces is still a very active field of research with important developments that took place in the last decades. In this mini-course we shall concentrate on the various minmax constructions of these critical curves and surfaces in euclidian space or closed manifolds. We will start by recalling the origins of minmax methods for the length functional and present in particular the “curve shortening process” of Birkhoff. We will explain the generalization of Birkhoff’s approach to surfaces and the ”harmonic map replacement” method by Colding and Minicozzi. We will then recall some fundamental notions of Palais Smale deformation theory in infinite dimensional spaces and apply it to the construction of closed geodesics and Elastica. In the second part of the mini-course we will present a new method based on smoothing arguments combined with Palais Smale deformation theory for performing successful minmax procedures for surfaces. We will present various applications of this so called “viscosity method” such as the problem of computing the cost of the sphere eversion in 3-dimensional Euclidian space.

Organizing Committee

Xavier Cabré​ ICREA and ​Universitat Politècnica de Catalunya
Gyula Csato Universitat de Barcelona
Amadeu Delshams​ ​Universitat Politècnica de Catalunya
​Filippo Giuliani ​​​Universitat Politècnica de Catalunya​
​Marcel Guàrdia​ ​​Universitat Politècnica de Catalunya
Tere M. Seara​ ​Universitat Politècnica de Catalunya

Scientific Committee

Scott Amstrong Université Paris – Dauphine​
Jean Pierre Eckmann ​ ​Université de Genève
​Jean-Michel Roquejoffre ​Paul Sabatier University
​Susanna Terracini ​Università de Torino

Poster session

Participants have the option to contribute with a poster presentation. The poster boards that are available at the CRM measure one meter wide by two meters high. Any poster size within these limits is fine.

To apply, please select the relevant option during the registration process.
  • Deadline: April 18th, 2022.
  • Resolutions will be sent before May 10th, 2022.


In order to increase the number of young researchers participating in this activity, the CRM announces a call for those participants interested in taking part in this activity. This grant includes a reduced registration fee and housing in a shared apartment on campus.

Application deadline for grants: April 18th (Resolutions will be sent in a few days)

The EMS offers some travel grants to young mathematicians from less-favoured regions within the geographical area of EMS membership for presenting results at conferences or attending courses, or for research stays in foreign countries, normally up to a maximum of 900 euros in each case or 500 euros for trips within Europe.
Eligible researchers should use this online form​ in order to apply for travel grants.


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.


*If the paying institution is the UPF / UB/ UPC / UAB, after registering, please send an email to vramirez@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 vramirez@crm.cat providing the internal reference number given by your institution and the code of the Project covering the registration (if necessary).

Lodging information



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For inquiries about the program please contact the research programme’s coordinator Ms. Núria Hernández at nhernandez@crm.cat​​