JISD 2025
21st School on Interactions between Dynamical Systems and Partial Differential Equations
JISD 2025
to July 04, 2025
The registration fee is 200€ / 75€ for granted and includes coffee breaks and lunch.
LECTURERS
SCHEDULE
POSTER SESSION & GRANTS
JISD PAST EDITIONS
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 di Torino
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
To apply, please select the relevant option during the registration process.
- Deadline: April 13, 2025.
- Resolutions will be sent by May 16, 2025.
grants
The application deadline for grants is April 13, 2025. |
Resolutions will be sent by May 16, 2025. |
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 |
Scott Armstrong | Courant Institute, New York University |
Jean Pierre Eckmann | Université de Genève |
Jean-Michel Roquejoffre | Paul Sabatier University |
Susanna Terracini | Università de Torino |
Name | Institution |
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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
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).
ON-CAMPUS AND BELLATERRA
BARCELONA AND OFF-CAMPUS
For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat
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